Molly, I am so sorry you are going through this right now. Dh's just don't understand and sometimes I wish Nigel spent as much time here as I do so he could see it wasn't that "abnormal" for babies to wake up to eat at night and that cio isn't the solution. I think your hypothesis might be right. If your dh is letting your dd cry it out for naps, she may have learned that she can't trust him.
Dr. Sears methods for getting your baby to sleep at night
Harvard study decries "Cry It Out"
Why don't you let your baby cry it out?
Crying it out causes "brain damage"
Night nursing and toddlers
These are few articles that might be useful. I hope they might help.