A. Trainers (even great trainers) are not necessarily behaviorists
B. I think rehoming this dog is the best option. I think you are right, he wants nothing to do with your daughter. It isn't fair to her, or him to force them to try to live together
C. I can't remember how old your daughter is, I thought three? (like my son). IMO, no three year old needs a dog for friendship. Wait until she is old enough to take on some responsiblity, and has some empathy for animals…five or six is a more appropriate age for getting a dog for a child. If YOU want to get a dog, that is another story...but don't do it because you think the child NEEDS a dog.
Thank you for your input. You seem very nice and knowledgeable. Yes it is I who wants a dog. Especially once Rusty is gone, I will be so lost without him. I have to give him 12-14 pills a day for his Fanconi, not to mention all of the water he consumes. At the same time my daughter LOVES animals. Her grandma has 2 dogs and she loves them so much, and they love her.