Thanks to all who posted some comments to my original post. Here are some clarifying points.
The idea that she refuses to leave her country or come to USA is a little overstated.
First, I told her (and all women that I make contact with) that I am free to live anywhere in the world, which is true. So this is not something that she just came up with on her own. i.e. the idea of staying in Ukraine.
Second, she didn't say she refused to leave Ukraine, just that she preferred to stay since I could live anywhere.
Thus the main point is not that she won't leave Ukraine. It's that she wants to work full time while living in Ukraine. That, together with my gut feel that most of her free time will be spent with her family or worrying about her family, is my main concern.
Further, I have not even asked this lady to marry me. We are both very cautious and analytical persons, and haven't jumped into the plans for or even talked about marriage at this point. But, we have discussed enough around the edges of a long term relationship that I have gleaned the info about her preferring to work full time, remain in Ukraine, etc.
Actually, I not even sure this lady is that anxious to get married to anyone. She was not on a MOB site, and we met through a professional relationship. She might be perfectly willing to have a long-term non married relationship, which would be fine with me. She was involved in a loveless (and even sexless for several years) marriage and knows that marriage does not go hand in hand with happiness. She was also in one of those marriages where the husband was less stable and successful in his work situation than herself and wanted her to earn the money and turn it over to him. So she also knows that marriage does not translate into financial security.
Yes, I am aware that the lack of marriage will mean she probably can't live in the USA anyway.
Right now, we are both extremely happy with our relationship, except we are not together full time. Her child has another year left of high school (after this current year). The child is very gifted and goes to a private Lyseum science school where they teach at a high level somehwhat like our Advanced Placement courses. When they finish this system they can go into third year courses at a 5 year university. She feels it would be best to have the child finish under the current system in Ukraine and get started in a university there before she can think about drastic changes in her life. I agree with her completely on this.