SSDI and Non-working Parent?

I was on SSDI before my ex and I broke up. When I moved out on of the first things I did was visit the Social Security office to see if I could get more funds added to the children's benefits, because I didn't think the current amount was enough to support them. In the two years now, that I haven't lived with them, my ex has yet to get a job, and has been living off of their SSDI benefits. Since she hasn't moved since we split, I know that her monthly rent exceeds the combined amount of both the children's SSDI checks.

Any time she starts to feel a pinch, (like when our daughter needed glasses, and more recently when she was/is behind in her rent), she calls my mother to complain that I don't pay child support, and that the SSDI isn't enough. Is there anything that can be done to ensure my children are being cared for financially? We never went to court for custody, or visitation, should I go that route instead?

By Michael B.