What state do you live? You said the father of your granddaughter lives with his mother in a 2 bedroom trailer but then you also said the father is your son. I am confused.
It would be a good idea to contact the Children Services in your state and see if they can give you some guidance and get them on your side.
If you have an attorney ask the attorney to request the court to require that the father 1. Establish parternity 2. Begin to pay child support and back child support 3. Drug tests
4. Parenting classes.
Chances are this father will not continue with these requirements and the court will not give him the child until he does.