A few months back I did the same type of research, although it wasn't primarily for backpacking, but more of a family dog that could also do some backpacking trips.
I have similar criteria to you as well: shedding, good with kids, friendly, etc.
I found an interesting breed of dogs called Labradoodles and Golden doodles. Basically they mix a poodle with a Lab or Golden Retriever. The type "B" variant can be the size of a Lab or Golden Retriever, but with the hair of a poodle. While no breeder will guarantee your dog won't shed, it's something to look into.
I haven't seriously looked into it, but do your research and find a good breeder. Expect to pay from 1k-2.5k and have to put down a non refundable deposit as well.