Being divorced and paying child support here in CA, if she takes you to court, you will have to pay her half of the child care. If you had child care, she would have to pay you half. Since your child stays with your mother, you do not have any child care expenses.
Honest, being civil to your spouse now will reduce the amount of stress you both have when/if you legally separate. You child will be much happier with life if things are calm, relaxed, and you focus on the child.