If a custodial parent were to remarry to someone in the military, what is the likelihood that they would lose primary custody based on relocation?

Scenario: The mother used to live in VA, divorced her husband due to abuse, but he was not convicted because it was the first documented offense, even though it had been happening for years, he was only placed on a two year probation. She then remarried a man in the military based in NC and retained the physical custody of the children based on the non custodial parent's background of spousal abuse. They don't have orders to move yet, but are concerned that if her new husband is stationed somewhere else, that she could lose custody of her two children by her ex husband. Is this something that could happen with his background, or would she be safe to not be concerned that she would keep custody because the move would be military orders and not just her deciding to move?

First, he had to be convicted of something, to get probation... Almost no one, actually goes to trial. About 95 percent of everyone charged with a crime, settles it in a plea agreement... That is still a conviction... So if he is on probation, he has a conviction for something

What does the legal custody papers from the court say... it appears it already allowed her to move out of state. What else was ordered? Normally once they move from the home state, if, she needs more permission depends on how the court order for allowing her last move was written and ordered

Actually, I was thinking more of a futuristic situation for my sister. So the situation is that she is separated from an abusive husband, living with our parents right now. Since they are legally married and only have a notarized separation agreement, would she have the right to move to NC (3 hours away) now? Nothing can be filed with the courts until next summer when they have been separated a year, so would he be able to stop her from moving out of state now? Also, would it be wiser for her to move now or to wait until after they file the divorce, since he has claimed that he will file for custody if she tries to move them out of state?