Yes, this is a good idea also^. But then again, cats will give birth outside in the bushes in freezing cold temperatures. You wouldn't leave them all there to die, would you? No, so sometimes, you have no other way around it but to get the family to a safer place, even if that means a little stress on mama. I don't know about you, but I'd rather the mama stress a little bit while transferring her and her offspring to a warm safe place, than let the entire family die outside when I know I could've helped. It won't be the end of the world, just stay calm and collected and swiftly transfer her elsewhere without it being a hassle. She'll settle down eventually, just try to make the new location den-like.
Good luck
Good luck