If you do move them, your in Steel Town it's COLD. Get some 2x4's, Armex or other sheet foam insulation an an electric oil heater. Build a temp rat room. Or go big with lights an water for a perm room. With the heater you can keep at 10x10 at 70f easy, but 60f is much cheaper. Yes, at 60f the rats won't breed well if at all. But they will be fat an happy.
Now, if you have mice in the house, they are in the garage also. Check alone the foundation an fill any holes you find. Then it's bait an trap the little guys
Good luck!.