Thanks to Rachel for explaining what a Nance appliance is! My child got a palate expander recently, which is different, but I do want to offer this idea: Go to an orthodontist rather than a dentist for another opinion; in fact, go to two orthodontists. Most orthos. do FREE consultations for children so you can go to several for nothing and get a feel both for what they think is best and for their personal fit with you and your child. Call and ask for a free pediatric consultation. (No, I don't work for an orthodontist!)
I'm sure many pediatric dentists do fine with ordering ortho-type treatments but I do know of parents who felt very pressured by dentists to get certain things done quickly, when orthodontists they consulted had different opinions or wanted different approaches or wanted to move more slowly. Even among orthodontists, treatment ideas can vary -- one wanted to yank one of our daughter's baby teeth immediately to make room, and another said that was not needed this soon(we went with the latter and things are going well so far). You may be more comfortable with whatever you choose to do if you get a few more opinions, and since they're free, why not do it? It's good to get this ortho. stuff started earlier in life, since their mouths are still forming and they'll have an easier time with braces etc. than their parents did, but you do have time to get some opinions. Let us know how it goes!