If you mean the housing projects military provided? If yes, even a Thai with non-military background/relation is not allowed. My father was a military personnel, I know for the facts.
There’s time until your moving date to get her Thai passport renewed. NA and LA, CA are just distance away, take her there and get it done. Or used her US passport to go to Thailand and get it done once over there. The fees are pretty much the same.
My two children were in the similar situation; been here since a young age and visiting when they were older. I’m familiar with the situation.
The new law; requires the POA to be stamped by consulate or embassy if the person is overseas. That’s my อำเภอ telling me and asked for when I tried to get my daughter’s household registered.