I don't want to seem harsh or unfeeling but military mothers know that they are responsible for making realistic arrangements for their children's care long before deployment. If circumstances with the care giver change, then the service woman needs to inform her chain of command immediately, and start making new arrangements.
I know my next statement won't seem PC but the truth is, "single" motherhood is part of the problem. The father should be equally responsible for child care, and I don't mean just the financial aspects.
Many of these problems go back to my long-time disagreement with sending women into combat zones (for about 30 years I've been saying that). Once the military started depending on women to make their enlistment quotas, they had to put deployment first and motherhood second. This has adversely affected families, and weakened the military.
When I was on active duty in the Navy, I had to request special permission to stay in while pregnant. Then, after my daughter was born, I had to put into writing that I child care arrangements available (primary and secondary) in case my duties required me to be away from home. (Women couldn't serve on ships or in combat areas back then.) When I later transferred to the Reserves, I still had to document that I had child care available. Since my husband was active duty military, it had to be a civilian other than him. This information was reviewed every year in case there were changes.
Whenever we went thru deployment exercises, or the real thing, each member went thru pre-deployment screening. Anyone who thought they might need a waiver (for health, business, personal, or family reasons) went before a board that would determine what they should do.
There is a procedure in place for these kinds of problems. One thing you never want to do is just take it upon yourself to leave or not show up. It almost always makes the matter worse in the long run.
In this situation, even if the mother doesn't want the father involved in the child's care (maybe he's a bad character), she should at least go after him for financial support. It's possible that if the father provided the money, the grandmother wouldn't have to run a daycare in her home, and be more available for taking care of the granddaughter.
Anyway, just my two cents.