No, Mama Murphy moved to Red Rocket for me all on her own. Not sure if you can move them manually but they definitely aren't tied solely to Sanctuary.

For the bed, simply store the bed when you finish sleeping in it and put it out when you want to sleep there. The NPCs cannot use what you have stored so they won't use your bed if it's in storage.

You can easily get through clipping by building with either of the foundation floor pieces because they are already designed to clip through stuff. There are posts here about it as well as YouTube videos.