Perfect Pals is the animal shelter? Did you even explain your situation to them. Maybe they would have something for her. I think you are shooting down ideas before really finding out what is possible. The only reason I keep trying is I worry about your daughter & this negative attitude.
Y'know, there are lots of good suggestions here. I agree with what someone else said: If she's unwilling to try anything, then maybe she should sit home by herself, hot and bored. You can't always cater to what she wants.
The animal shelter here has a thing called "cat socializer". I knew a kid who did that. They gave him the cats that were very shy. He sat quietly in an empty office & waited for the cat to come to him or get used to people. Sometimes they do that for dogs, too. They have a guinea pig right now they need someone to sit with it & cuddle & 2 rats that like to be read to (childrens books are OK) and petted.
I have offered my boys options but if they choose nothing, then they have to deal with it. When they get bored enough, they find other things to do. They even go back to kid stuff like legos or Dr Suess books (one is not a good reader).
If she really is this negative about everything - maybe she should have a workup for depression.
My kids have had friends that have had injuries and couldn't do much but they do what they can. They watch there friends games, play cards or board games, sit at the pool & put thier feet in, go to the mall & let a friend push them around in a wheelchair, drive the electric chair & grocery shop with mom, etc. A normal 12 year old would find things to do.
Remember when she starts whining that she is bored - The bedroom door closes and you can turn the TV volume up.