How to deport my wife?

A very familiar story. I assume she has a permanent resident card as opposed to the two year temporary resident. If she still has the two year, deportation would be much easier. However, if she has the permanent resident card (10 year) it is more difficult to deport her. I am not giving legal advice here, just passing on what I have read as I am going through a similar situation. If she has any criminal record, that is where you want to start. Even a crime such as shoplifting carries a major penalty as it is defined by immigration as "moral turpitude". As I understand it, one of these violations in her first five years of being in the states with a possible sentence of one year (even though she may not actually receive that sentence) wins her a free boat ride back to China (or wherever she's from). But it is possible to get a waiver of deportation from the judge for this if she has "extenuating circumstances. But more than one conviction, regardless of potential sentence or how long she's been in the country also guarantees deportation. Waivers aren't possible with this method.
Now the bad news. My wife has four shoplifting charges. She had two when she applied for citizenship and was denied (but not deported). She now has two additional shoplifting charges which should be more than enough to get her deported. But it seems immigration is only concerned with illegals rather than those who break the law constantly while on a permanent resident card. Oh yeah, she also lied to get a Pell Grant (she already has a BA and MA from Mongolia) and the government isn't doing anything about this either.
Conclusion, if she isn't breaking the law, you're gonna have a real hard time deporting her. As you can see, even if she breaks the law on numerous occasions the government doesn't seem to want to use their time unless it is felonies despite their own rules and the LAW.

You are not the victim here. Everyone who marries a foreign national knows that US citizenship is often a factor in the relationship, especially with a 30 year difference in age. If she leave the country with your children you will be in a no win situation. You may be the better parent but you are also 64 and she is 35. Age will play a factor in custody. You have a domestic problem. Involving immigration will only make things worse. I would try to make a living arrangement that makes it a positive environment for her to want to live near you so your children can be in your life. The children should be your objective. having a relationship that works for both of you is in your best interest. The alternative is a winner take all approach. As a father who lost my child in a transcontinent feud I can tell you any amount of children in your life is better than 100% of nothing.