A.R.
Yes, if you don't get Prime you will lose the free movies. You might be able to link your kids Fires to you Mom's account, but you would have to log on to her account to manage any content on their Fires.
I have a Fire and Prime, but don't use the free movies too much at this point since I mainly surf & read on it. I have Prime for the free 2 day shipping, not movies.