Late, re your mum looking after you, I'd go with your instinct. I didn't need looking after post extraction and I think the transfer is more straightforward. I did have to have someone collect me from the clinic post extraction because of the sedation (I was fine, but the clinic required it). But both times I then went home by myself, once we'd established I wasn't going to keel over. Both times I would have been happiest just chilling out and napping, but the first time around I went out for dinner later because it was arranged and the second time I had to do some work from home later that day. I didn't feel great but it was manageable. First time I had quite bad cramps (equivalent to moderate period pain but more constant) and the second time I had less cramps but felt more nauseous.
Personally I find having to deal with other people's emotions more difficult than dealing with my own, so I would also want the space to be by myself, or maybe have a friend who has less emotional investment than my mum!
I did feel quite vulnerable and nervous going for the first extraction and I did sort of wish I wasn't by myself. But the staff were all lovely and reassuring - I told them I was nervous and the anaesthetist said he would deal with that! I'm not sure having someone there would have helped because ultimately they couldn't have the extraction for me. I did find myself thinking that it was probably good preparation for having to deal with some difficult stuff solo after the baby is born.
I'm not sure what I'll do for the eventual transfer but I don't think I'll want to make a major deal of it because here's still so much that can go wrong.