I agree about giving her time to adapt. Also, when she starts that pining trick, as hard as it is to not do it, responding with reassuring words just reinforces the behaviour and makes her do that on purpose...just for the attention. You're sort of praising the "Sad", behaviour and so encourage it to go on even when she isn't sad, she'll act that way to get a response because she knows it works.

Dogs are adaptable creatures but she'll not learn to adapt whilst she is being praised for sitting there and whining, she'd rather carry on doing that instead.

Sounds harsh, I know. Don't give up on the wheelchair thingy and don't take her away from the other dogs. They seem to get on ok and she isn't scared of them...just ignoring them a little. She'll start to interact more once she gets used to spending time with them again.