I think they'll be ok moving twice - not happy, but they'll adjust pretty quickly Mama more so than Blanco, I imagine. In a small space, you can give them more room with one or two tall cat trees and/or shelves on the walls. If you have two bedrooms, maybe you can make one Mama's safe room?
If you have several toys that Blanco can entertain himself with, and places he can climb to, it might be easier for him. The cat tree(s) should be in front of windows so he can look out (but hopefully not in a direction where there are any cats outside). I'm often too busy to play for long periods, or if I have time, no one feels like playing. Margaux would never, ever play by herself. I had to be attached to the other side of any toy for her to have any kind of interest. But Celia will bat the squeaky mouse that hangs over the door or the ball in the ball-in-circle toy. I know you said he's fat, but a treat ball might keep him occupied if other toys don't interest him.