Thanks for the chance to help. I am an attorney with over 12 years experience. Hopefully I can help you with your legal question.
This is something you can request the court to address. And a lawyer would be very helpful (it would not be helpful to "ask" the judge on your own...you need a lawyer to file a motion with the court so the judge can consider the issue)
Lets start with some background information...
Under current military policy, they are not taking "single parents"
This rule applies for induction alone...once a parent is enlisted, they can request to modify custody...and the military will not (actually can not) do anything to prevent this)
So your son needs, at this point, to modify custody to allow him to enlist.
And this is something an attorney can do for him...can file a motion with the court and explain to the court what is needed (that his custody be modified so he is not a custodial parent
But the court is not going to give the rights fathers rights to the paternal grandmother...not unless there is some issue with mom...in order to give custody to a grandparent, the court would need to find both parents unfit...what you describe does not sound like that is the case.
That said, CA law WILL allow grandparent visitation. The court (the same court that is addressing support) can grant visitation to the paternal grandmother. Not the same as custody...but time with the child regardless. In order to obtain grandparent visitation, the grandparent must prove that visitation with the child would be in the best interests of the child. With dad preparing to enter military training, that should not be too tough to prove
SO, what you describe, I would have an attorney that can ask to modify custody (in favor or mom) to allow dad to enlist, and at the same time grant the paternal grandparent(s) have visitaion
Please let me know if you have more questions...happy to assist if I can