Is it just you and your mum in the house? It all depends on how willing your mum is to adapting to the two fluffballs. I think in the long run, the birdies would be happier in an active space where they can see your mum going about her business, maybe your living room is a brighter more sunlit space, the tv would provide entertainment etc etc. So the routine could be daytime in the living room, evening in your bedroom where I assume it's quieter. But it depends on what it's like in the living room, the birds will need time to adjust to all the new stimulus.
As for bird proofing the living room, you said they don't really leave the cage. So in that case, there's not much bird proofing necessary. If they do have out of cage time, then it's just common sense about what to bird proof. Mirrors can be dangerous because birds can fly full speed into them, same with windows, but typically it's not an issue once the birds get used to the windows (it's a big danger when they are first released into the room as they don't know the window is there). My two have had very gentle bumps into the window at the start and they've not done it since. Any areas the bird can become trapped or entangled, like if there's a bunch of wires or something. Not a huge deal though since your mum is at home, so if she's attentive, she'd notice if one of the birds was missing and caught somewhere.
