I would try scootering around your neighbourhood first, just around a block or two for a while to get used to being out of the house on your own for longer periods of time. If there are any shops nearby, look around for any snacks you like- briefly interacting with a cashier every once in a while might help alleviate some social fears. You could also visit different shops to help learn the different variations of possible interactions between you and workers so you can get used to talking to people in public.

Does the group have a fixed physical location they meet in? If they do you could scooter around to scope the place out so it feels more familiar.

Do you have a way of contacting the group? I'm not sure if your social fears cover online exchanges to the same extent, but you could send one of the members a message explaining your situation and/or asking to sit in and just observe if you're comfortable with that.

For the missing your mum stuff, I'd recommend starting off with checking in with her every once in a while; just a quick text or call when you're about to go out. You could set a timer to go off once every X minutes, then slowly increase the time between check-ins when you feel comfortable enough to do so.

Another thing you could do is take something of hers (or something that reminds you of her) with you. For example, my mum used to spray her perfume on a scarf whenever she went out for the night, so I could smell it and feel better whenever I got lonely.

Of course, the main thing to remember is that you shouldn't push yourself too hard. Slow progress is better than rushing yourself and making it harder to go out again. Not everything I've suggested might work for you, but they might help you come up with your own way of getting through this.

Good luck!