The IRS does not follow state custody orders or court disputes. The federal tax law says that, for children under age 19 (or full time students under age 24) they can be claimed as "qualifying child" dependents of a parent or grandparent where they live more than half the nights of the year. There are a couple of other items, but the fact that you pay some, or even most, support, is not used in the determination.
So the question is, where did the children live more than half the nights of 2025? If with you, you are allowed to claim them as dependents. If your mother in law, then she is allowed to claim them as dependents. If the children did not live with either of you more than half the year (like, maybe they lived with their father for 3 months, you for 4 months, and grandmother for 5 months) then no one can claim them as "qualifying child" dependents, and we would need more information to determine who can claim them as "qualifying relative" dependents which is the other classification.
