When you marry the proposed dad (or your mother) you can approach a court about step-parent adoption. Unless and until that happens, why would a court believe that either proposal is in the child's best interest or would provide stability and support?

There's no magic form that the father can sign to make the rights and obligations of parenthood disappear.

If dad doesn't want to be part of his child's life, nobody's making him. If you don't want his money, nothings stopping you from returning his child support payments.