What is Alexandra doing there anyway? She's not a band member, she doesn't work for them, and she doesn't serve any useful purpose. She mainly causes trouble and throws herself at Alan. Why hasn't she been shipped home?
She was in the comics.
But so was Pepper, Valerie's predecessor, yet she's not in the cartoon. There's no in-story reason for Alexandra tagging along.
Maybe she's there because it would be too much trouble to make her quit following them around?
Maybe she bullied her brother into it.
Why does Valerie play tambourine as opposed to, say, guitar or keyboards?
Presumably because every cartoon band of the time had a tambourine. The 2001 film at least had her be the bassist.
It's interesting to think about What Could Have Been it seems most of the "who plays what" in these cartoons were made via animation decisions (the tambourine is a pretty easy instrument to animate someone playing, etc) even though it rarely reflected what the actual musicians they had record the songs were using. Given the multitude of people good at music at Hanna Barbera, there really is some lost potential that they probably could have made some odder arrangements and rocked them.