Can my son be deprived of seeing his baby just because the baby's mother won't let him for no reason?

My son has a 9 month old son. Before the baby's mother got pregnant, the relationship of my son and her was already unstable. They broke up at one point and then she got pregnant by him. He decided that he would stay with the girlfriend through the pregnancy and through the first year with her to make sure the baby was ok. The relationship was going to put on hold. Recently, my son couldn't take their relationship anymore and left, though being a loving and responsible father since he left, visiting the baby, taking care of the baby and giving the mother $500 a month. Twice now he was not permitted to see the baby first by the baby's mother, and the second time by her and the parents. All he wants is to spend time with him. The baby's mother said "Let's just wait to see what the courts say". What are my sons rights to just be with his baby. He is not a deadbeat father who is disappearing, but only begging to be with his son. Please help.