ARRGGHH! The dreaded ever watchful eye.....an instructor, bystander, you name it - someone is always watching. Don't you know that Murphy's law says that when you have somebody watching you, your horse will do everything in his power to make you look like a ding dong. That's just the way it is (at least in my world...LOL!)
I say go back and get some riding time in by yourself on that other horse WITHOUT the ever watchful eye, and take a friend and just make it a fun day. It sounds like (i might be wrong) that your every move (for the most part) is maintained by the trainer and you don't get enough free time to venture down your own horsie path of self-discovery in riding?
And no, it is not too much to ask to have a sane and FUN horse to ride. If it is any other kind, then it isn't fun! And for what it's worth, I think it is great that you are riding with your daughter (something constructive to do together)...mine grew up with horsies (whereas I craved them forever until I got my first at 14) and she is completely immune to the horse bug....maybe my youngest will get bitten. One can only hope!