Hemyock, first please allow me to gently point out that there is no "the" in Ukraine. Back when a region within a larger Russia it fit. Today "the" fits about as well as it would in "the Canada" or in "The France." The constitutional name is simply "Ukraine." Thank you for allowing me to point that out. Some Ukrainians find it irritating and our job here is to help you travel as smoothly as possible.
I have found from living in Russia and Ukraine that how we men respond to the ancient traditions that many, even most, families observe is read by her family as a direct reflection of whether or not we respect her background and her family in general. Therefore I take a distinctly different tack and don't try to ignore the realities of her culture.
My desire would be to approach her family in the same way a local guy would for marriage. There are some country differences, even some differences region to region, and religious traditions observed by many families. So here is a copy of something I posted back in August and you should search the internet or ask your lady about traditions specific to her region.
Ukraine for example has traditions ranging from stealing her shoe on the wedding day, to riding a log in some regions. What does she say about it? Unfortunately many Western men march into a foreign country having taken over the task of wedding planner for God knows whatever reason....as if we were professional wedding planners back home. Goodness, speak of "control!"
In my case I met a lady in Moscow in connection with my work and was promptly informed that she didn't date. I had to learn courtship instead. Then also learned that she didn't like me. Well, she had to work with me and over time I could sense her change in attitude and growing interest. She is my wife today so I learned what was "proper"--because her family expected me to follow the rules. They saw no reason to deviate just because I was American. She had other men interested so if I didn't want to accept their culture, then I could move on down the road. She felt the same as her family by the way, but I later learned that she was secretly hoping that I'd be man enough to step up and learn about her culture so that we could court.
The advantage of Eastern style courtship is that it eliminates all competition. Our youngest daughter is 19 and in a courtship as we speak. She is a student at Moscow State University and a young man who is interested approached and asked our permission. After checking with the daughter to find out her wishes too, we consented. This eliminates all other competition. This guy can make it all the way to marriage with no outside interference if he plays his cards right. If not, he's eliminated and it's "next...."
Some of the conditions must be to complete his education (he is at the same school), show evidence of a job in summer, some savings accumulated (yes, I want to see bank statements. He isn't Donald Trump but he better know how to pay bills and manage money cause our daughter isn't going to starve cause she married some chump), and as the wedding is being planned we'll work with his family to obtain an apartment.
By the way, his family approves of this arrangement and practiced the same on a daughter they married off 2 years ago. And we're not part of some strange cult either--just ordinary practicing Orthodox. We just married our eldest in August in the USA and she and her new husband had to do the same. Girls usually love it because it takes the pressure off in many respects--he either makes it or we move on.
He is spending time with our extended relatives and they do the trips to zoo, hamburger at McDonalds with smaller cousins, outings to the Museum (with Babushka), and all sort of fun things. What he does NOT do is honk a horn while she runs down the lift and they take off unseen for hours. Doesn't mean they can never be alone, and she isn't fitted with a chasity belt (unless her mother did one without asking me--just kidding), but the focus is on whether he can blend with this family--not on how often he can get her off by himself.
Now not every Russian or Ukrainian family still does this to the same extent. But surprisingly to Western guys, more do so than you'd ever imagine. And believe it or not I've had Western guys call me all sorts of names when mentioning something like this. My response is to offer to take them to any city, any city, in Russia and Ukraine and we'll find multiple families observing similar traditions within 24 hours of arriving. It's not my rules, I'm just enjoying what I've learned. Western dating customs are just that--Western.
My wife and I did the traditional route as practiced by her family, and there are variances according to region, etc, with old style courtship instead of western "dating." Her father had died years earlier so after a year plus of courting with lots of family around, walks in park, going to book exhibitions with cousins, and all sorts of family outings instead of dates (she was mid 30's and I mid 40's) my future wife set up the traditional meeting with her mother and a trusted Uncle.
In an traditional setting the man doesn't do the asking--he brings along a representative to speak on his behalf, usually an older relative. I didn't have any relatives in Moscow so one of her cousins (younger but close to my age) agreed to be my representative (all those family times paid off) and all I had to do was bring the required bread and vodka and answer questions from her Uncle and Mother.
As a signal that conditional permission had been granted, mother took the bread to cut and serve, the vodka was opened and my future wife was then permitted to come into the same room to join us. She brought out the traditional wedding towels upon which we would stand at our church wedding and which are used later at the baptisms of future children. The final condition set by her mother was that the family priest approve so I still had to meet with him. That wasn't a problem since I had been attending to the same Orthodox church in Moscow for almost a year, but it was still a condition and he could have nixed the wedding.
I surprised her cousin by bringing along chocolate in addition to the bread and vodka, explaining that we needed all the help we could muster! I think it was the chocolate that put us over the top.

No engagement ring--she didn't want it because its not traditional. Being Orthodox we wear our matching rings on the right hands. In Russia a ring on the left hand can mean that you are a widow/widower/divorced but again looking.
Usually worn at first in order to make the guy happy, over time most engagement rings end up in a dresser drawer and that's not exactly a smart investment on the guys part.
We had a ZAGS wedding (it's RAGS in Ukraine) and then later a church wedding. Go to YouTube to see Russian or ZAGS weddings. For a 10 minute or less ceremony, they're extremely fancy (in most cases), important, and structured.
There is no "engagement" in Russian culture and the "betrothal" happens at the very beginning of the church wedding, just inside the entrance where the priest hands the rings to the couple to exchange. After some prayers and choir chants, the couple with their hands bound together by a thin wedding towel, move with the priest toward the front altar area to be "crowned." Later the priest leads a procession of the couple and attendants three times around an altar. There are no vows in a Russian ceremony, in fact after answering a couple of questions (as to are they legally free to marry) by the priest at the entrance of the church, the couple do not speak thru the remainder of the almost hour long ceremony.
There are no bridesmaids or best men in an Orthodox wedding, just two sponsors/attendants (one for each) who hold crowns over their heads (without touching) thru the liturgy. As the ceremony is a holy sacrament they drink wine from a common cup 3 times administered by the priest. The couple holds candles during the ceremony. Their hands which were tied together during the ceremony are unbound when the priest presents them as husband and wife. As with most Orthodox liturgies, the majority of the ceremony is done with everyone standing. There are no musical instruments used and everything, from readings to songs to chants are sung, not spoken.
At ZAGS (RAGS in Ukraine), the officiant directs a 10-12 minute ceremony at which the rings are exchanged near the midway point. We had both weddings since church weddings in Russia are not legal events.
We stood on wedding towels with one towel binding our hands also. The "master of the home" was accomplished at the wedding party with a large wedding loaf, which is a round baked bread and ours had designs of a cross baked on. In the center was a round hole at the top and a small cup of salt was inserted. Each broke off a piece of bread (the biggest piece determines who is head of the home), which was dipped into the salt and immediately eaten. Our eldest daughter and her new husband did this tradition also in their August Russian Orthodox wedding in the USA.
I like the traditional symbolisms: One common loaf baked by the two familes illustrates a new family as one, but retaining the connection back to our families. Eating the bread together illustrates that now all things in life will be done in common. The salt illustrates how life is not just sweet and tasty but also has it's bitter moments (saddness and sorrows) which are now shared as one.
Some couples take the towels they stood on during the wedding to place on the floor to enter the home for the first time. Other couples have different traditions. I just believe it important not to assume that a wedding there is the same as one here and that proposals there are the same as we do them here. They're not, and even if you don't live there, the more you can do to honour the things her culture finds important, the better relationships you'll enjoy with her family long after the wedding day is over.