I'm so sorry that things didn't work out for your son and daughter-in-law, particularly in light of the children. The chances of him winning custody depend on a plethora of factors, many of which you do not have access to. However, there are many things that if properly investigated and presented, could assist.
First would depend on whether he is seeking joint custody or sole (joint is easier, usually) and whether he is seeking primary residential custody of them, with the mom having the visitation. Assuming they will not be agreeing, then other details have to be evaluated, in generally concerning what will be the best interest of the children. In the past, the tender years doctrine favored the mother when the case involved very young children like your grandchildren, but this is generally no longer the case. Also, where and with whom the children are currently residing is also a factor, particularly if it has been of some duration, status quo seem to have some strength when it comes to avoiding disrupting the routine of the children's lives.
The mother's illness could be a factor, if it negatively effects the best interests of the children. Of course, that depends on whether she has it medically under control. If it is controlled, it would be less likely that she would get points against her due to this disability. If it is not controlled and there is appropriate proof of a violent propensity, this could be strongly in favor of your son. (Keep in mind the possibility of 'supervised' visitation' if she is a potential danger.) Did your son file domestic violence charges against the mother when she inflicted the physical violence on him?
As you can see, the issues and proofs are many, and we only touched on some here, in light of the limited information. I am very glad that you son is seeing an attorney tomorrow, because when it comes to custody, doing it right from the getgo is very important.
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I wish you and your son and grandchildren the very very best and hope it works out as it should.