My husbands ex-wife has custody of the children, and didn't let him see them for over a year until he took her to Court. Now we see them regularly. She called my husband recently and told him she wanted to work in another state and go to school there, but the real fact was that she was moving because she met a man. He responded that the divorce decree stated she cannot take the kids out of State. She left anyway, and the Courts made her come back. Now she is saying the same thing again, school, work, etc. but again it seems it because of a man. She contacted him a week ago and said she was leaving, she would drop the kids on the doorstep and wouldn't come back for 3 years. Isn't this child abandonment?

First, its not a good idea to piggy back your question on another thread. To avoid confusion I've moved your post to its own thread.

No, its not. Abandonment is a criminal offense that involves leaving the children without adult supervision. That is not the case as you describe.

However, if she does do this, your husband should immediately file in court to modify the custody order. Petition the court for three things:

1) That he now has, at least, primary physical custody. He can try for full physical and legal custody, but I doubt if he will get it. He should try to have control over visitation, so that she has to schedule any visitation with him.
2) Since he will have physical custody, and support obligation should cease immediately.
3) Since he now has physical custody, that the mother should start paying him child support.

Number 3 may not fly if she has no source of income, but he should still apply.

Agreed, it is not abandonment, it is merely family law issue. He needs a great lawyer and fight to get children returned