CPS looks for a family placement first. It's better for the child to go with people he/she knows, and of course the state doesn't want to pay for foster care if they don't have to.
A family member would get a criminal background check and quick look at their home, at least. For example, the relative a child is placed with can't have a serious criminal record or very substandard living conditions. CPS wants to be sure they're not leaving a child somewhere as bad as the environment they just removed him from. But the standards aren't as high for a family placement as they are for a foster parent, who must take classes and go through more thorough investigation of their home and background to get certified.
A father who was in continual contact with his child would most likely get (temporary) custody of the child when he came back. A child's parents usually have the most rights, not the grandparents. However, once CPS is involved, they're in charge, so transferring the child to him would go through them. He'd at least get that preliminary screening and I'm sure they'd want to know why he was incommunicado.
Also, the mother would get a chance to get the child back. They come up with a plan that includes what she would need to do (usually it's counseling, parenting classes and fixing whatever problem led to the removal) and a time frame (usually 6 months, to possibly be extended to a year if she is making good progress). It also includes a back-up plan of what will happen if the mother doesn't meet the goals. If the father is deemed fit for parenting, that would probably mean he'd be the one to get the child if mom doesn't get it together within the time frame. Also, the placement decisions go before a family court judge for finalization; it's not solely up to CPS.
And then, of course, the father could go to family court to try to get permanent custody anyway, and it would be up to the judge. If it was granted, CPS would be out of the picture.
Oh, as far as the mother being coerced to sign over custody, no, if there's cause they take the child, on an emergency basis. Frequently, the police are first on the scene and call CPS (for example, if they take the mother to jail). Her consent or signature aren't required. The CPS worker gets approval for whatever he/she does from her CPS supervisor. It then has to go before the family court judge within 3 days for final say on the temporary removal and placement.
Sorry for all the edits. I'm not awake yet.