Husband filing for divorce and claims mental abuse can he have a restraing order and have wife and children evicted?

Most likely not for mental abuse, he can file for divorce and ask for the eviction in housing court. But then the court may allow the wife and kids to keep home.

I wasn't sure whether this belongs in Family law or Real Estate Law, but it sure didn't belong in Immigration Law where it was posted.

There is a possibility that he could get a restraining order. But more likely he would be required to move until the divorce is final.