Me and my Ex-husband have joint legal custody of 2 minor children. I am asking to carry 1 of the children on my income tax and I am willing to let him carry the other child. I was told that by law I can carry 1 if I have them enrolled in school, but he is not willing to do this. I buy everything for my children when they are in my custody and he does not help in any way,when they are with me.

You may need to have it written in a court order who gets to claim the children as dependents or whether you will split them. Generally, if you provide the bulk of their care, and they live with you most of the year, you can claim them... unless otherwise noted. It's not up to your ex whether you can do it or not... might be wise to seek legal counsel if you can't come to an agreement.