If my x-husband has clamed our children on his taxes when he wasn't suppose to. What are my legal rights?

Hi,
Welcome to this site; and I know you will get many answers to your question.
Does your Divorce papers say you are to claim the children? Or anything in Separation Papers (if no Divorce papers) say you can?
If so, I would claim them. If IRS has any questions about it, they will contact you. You can then offer them proof, and they will definitely "back up" and check into your ex's tax returns!
Here is a link with the same opinion:
http://www.taxtrimmers.com/taxfaq/daughter.shtml

Also, here is another link; look under the Frequently Ask Questions, #4. If you are the Custodial Care person for your child (children), then your ex cannot claim them, even if he is paying child support.
http://www.sbls.org/etaxfs3.htm

I do wish you the best.

Claim them as you should. It may be that you are questioned about this by the IRS, but nothing for you to worry about.

He will be the one with the big problem.