I am in California as well and been in the court a time or two so here is what the Courts take on it will probably be. They will not take baby from mom unless she is unfit. To prove her unfit would be almost impossible. Unless she is a drug user who leaves baby alone, uses drugs and breastfeeds or is abusive you aren't likely going to prove her unfit.
If she is eligible for welfare, whether dad agrees with it or not, then she can be on it. Try to take the position that her being on welfare is better for the baby for right now. Baby is with mom where he/she should be not with a sitter. She may be perfectly capable of working but if she can be home with baby full time that is what is best, especially if baby is breastfeeding. She can go to work when baby is older and not so terribly dependent on her.
Your son should not take baby to far from mom right now because of breastfeeding in particular. Two hour visits a couple of times a week are appropriate for now. Although some babies handle switching from bottle to breast relatively fine it is not the best route to go with. It can cause problems and then she may have to stop breastfeeding entirely. Which I am sure you all would be happy with so that you can have baby more but that isn't really what is best for baby.
Whether he is staying nights or not he can be ordered to pay child support. All she has to do is go open a case with the DCSS.
You said your son wants to get baby out of the bad environment she is in, what is so bad about it? That information could result in different responses here.
What your son needs to do is hire a lawyer. Truly. Without a Voluntary Declaration of Paternity he will probably have to submit to a paternity test first off. So he will file a motion to Establish parentage. Then he would need to file an OSC (Order to Show Cause) asking for a custody/visitation agreement to be made. Specifying what he would like to see the arrangements be. His lawyer will be able to better let him know what he should ask for based on the specifics of his situation. But as a general he should try to come up with a "step up" plan. Which will start with a minimum of time gradually increasing every six months or so. Speaking to a custody expert will also be great for your son to find out what time share plans would be appropriate for different ages. Courts rely on custody experts a lot for guidance as to what should be ordered. If she contests and does not mutually agree outside of court then they will be ordered to mediation. Mediation will be held by the Court with a LCSW (Licensed Clinical Social Worker) or a MFC (Marriage & Family Counselor). In mediation it will only be dad and mom, no lawyers. Each will be given the opportunity to tell the mediator what they would like to have happen and the reasons for it. The mediator will try to get mom and dad to come to agreement during the meeting but if they can not then the mediator will decide what they feel is appropriate and write it up for the Court to approve. The judge may or may not agree with the mediators suggestion/opinion but more often than not the judge does go with the mediators decision. Custody battles can very VERY (mine was $28,000 on my side alone) costly so ask your son (and yourself since you are helping him) to think very carefully before asking for a custody/visitation arrangement the Court probably won't order.
Here is a web site with a lot of very helpful information:
http://www.divorcenet.com/states/cal...sitation_plans
There are "sample" plans on that site that I KNOW the court in California DOES order in different cases. I hope you find the info helpful.
Just make sure you have your son and yourself always ask yourselves "is what I am wanting THE BEST for the baby or is it what I want? Good luck!