I'm very sorry for your loss. It's difficult to lose them - they just have a way of wiggling right into your heartstrings. I also do understand that you don't want to take on more animals than you can handle. She has a buddy right now, so I wouldn't worry too much if you are able to provide her with enough attention and play that she isn't hassling the elder lady.
Something I recommend, if you haven't already to help with that, is to add a wheel (none with gaps where their tails can get caught, though!) or hang treat balls/toys from the top of the cage so the youngest can run and bat things around and stretch as much as she likes where she feels safest.
Meanwhile, keep bonding the way you are with her. Keeping her in hoodies, just letting her ride around while you make food, coffee, tidy, etc. so she can both get accustomed to you and the smells of the environment before additional free roaming time. It'll help her get comfortable and she may be less nervous come the next time she is taken to the living room.
For bonding, offer her little treats and/or nesting materials by handing them to her while she's inside the cage, since then she begins to associate you with super good things. My boy doesn't care about this whatsoever, he just wants head scratches and hugs. My girls go bananas if you try to gift them things. Also - if it's possible - sit by the cage with the cage open, and just talk to her/hang out/do what you do (play a game, watch TV if possible, listen to music, whatever). We have one girl right now who insists that we don't pick her up; but that she climbs out of the cage onto us herself. If she skitters up our arms or dives into our hoodies, that's fine. But if we try to pick her up? She hates it. Of all the rats I've had over the years, she's the only one who demands that level of independence. Meanwhile our [neutered] boy begs to be picked up. Your girl may just have very different preferences for handling than what your previous rats did.