What to do about son/grandchild drama?

My son has a 4 year old daughter. He is no longer in a relationship with her mother. He has tried many times to get back into the relationship, but they only stay together for a few weeks. Well, the last time they were together, she told him she was pregnant again. She treats my son like dirt and when they split up the last time he told her it was for good. He had talked with an attorney about setting up some regular visitation for his daughter and the baby that is coming, but they decided to wait until after the baby is born before they serve the papers on her to go to court. The children's mother does not know papers are coming. My son has spent several months thinking that the second child is his. But the doctors keep adjusting the due date. He questioned the mother, who finally admitted that she isn't sure who the father is and they will have to do testing. She was with another guy just before she and my son got back together the last time. And then when he moved out, the other guy moved back in within 2 weeks. My question is--how do I as the possible grandmother deal with this situation? On one hand, I feel sorry for the girl, although I know she put herself into this situation. I have given her baby clothes for the baby boy due to be born around July 4. It will tear my heart out if I bond with the baby and later find out that it is not my grandchild. Or if I don't make an attempt and then later regret not trying because it turns out to be my grandchild.

My questions: How soon can a paternity test be done and how quickly do you get results? (I'm sure she will be wanting to collect child support, so a test will have to be done anyway) I've told my son, not to agree to have his name on the birth certificate or sign any paperwork until the test gets done. The other potential father is a married man.

Another question--If you were in my place, how would you handle the situation?

Thanks in advance for the suggestions and advice.