I have Border Collie's and your dog unless your dog is socialized he will continue to do this. I agree with the above poster, but I want to suggest you take it one more step and take him to dog training and angility class with your daughter, so they will form a bond. You won't need to do this for a long time as I hate for anyone to spend money they don't have. I realize your dog is a mix, this behavior is seen in BC's more often when they have not been around others. Good luck.
I think it more about you then her it seem like the pack order is out of whack it seems as if he has claimed you has his.Your his and he says who and when yourdaughter can be around you.Why, he loves her when your not around and when your there your his and he will not let your daughter been around you or play with him.You need get it back in order her are a few suggestion on how it might help when you on the couch or anywhere in the house sit down invite him to sit with you have you daughter come in has soon as starts to growl get up say no leave the room and ignore him do this over and over a couple times a day when he clam down and doesn't growl have you daughter give him a treat and and praise him hopeful he will start to realize he get no attention from you when he acts bad or growls and when he is good and with you he will start to view your daughter as the good a thing instead of a threat.Hopes this helps.