
it does sound as though Pickles is seeing her as under him. I would continue all feedings done by your daughter. Even have your daughter give him a command like sit and if he doesn't sit (only say it once) you make him then your daughter rewards him with a treat/praise. Another one is pick up all toys and have your daughter give her a toy and only allow play time with the toy for a short period and then have your daughter remove the toy (of course with you there), but when she takes the toy use a command and treat/praise or offer another toy. This way Pickles won't have a problem giving things up because it means he will still be getting something. Do you allow Pickles on the couch? Who's top dog Pickles or Dolly? I know hard to tell since he is so little right now still a baby. Maybe don't allow Pickles on the couch and only pet and cuddle him when you and your daughter want to NOT when he wants it. Yes try to have your daughter do lots with him so he learns that she is above him and not a playmate. Always supervise play time with the two of them at all times.
My children use to trip over Tiva (boston terrier) she was really tiny at 8 weeks but I never had the problem of her going to bite or growl. They did stick their hands in her food and feed her but they also did this with all our dogs, even the puppies we had.
Pickles could be scared because of her tripping over him but hopefully things will work out...Good luck :)