I am the mother of two kids which my mother has custody of, how can I sign my rights away to her and will I still have to pay child support?

She will have to adopt, so if she is willing to adopt the cihldren and you and the bio father will sign to allow the adoption,

But you can not just sign over custody like you are selling a used car

You can't sign over your rights. Only a court can terminate rights. Courts are very reluctant to do so. And they will not issue a TPR just to let a parent out of paying support.

Since your mother has custody, I don't see a court having a reason to terminate your rights.