Please listen to the orthodontist. Some dentists "do" orthodontics but unless your dentist has a specialist degree in orthodontics as well as dentistry, why would you go with a generalist for what is a specialist service? An ortho. deals with appliances and braces and moving teeth all day every day. A dentist who does ortho. is not doing it as often as an orthodontist and just won't have the same level of experience.
Do get a second opinion from another orthodontist. In our area tons of kids start the procedure for spacers, expanders, braces etc. as young as seven or eight and it's very common here for parents to see at least two orthodontists for initial treatment opinions. It's just good due diligence on your part because some orthodontists are more aggressive than others, some love to pull permanent teeth while others want to wait a bit, some are good at specialized appliances and others don't have a clue, some may think things are worse than others do....So get two opinions. It is free to get an initial consultation so why not?
We had two orthodontists tell us two different things to start and the main difference was that one wanted to start yanking out teeth right away. The other was more conservative and tries not to pull teeth especially right at the start. We went with the second one, who also had a plan for dealing with our child's fairly rare issue of "reversed" teeth that came in but were in the wrong positions. The first orthodontist didn't even mention our kid's reversed teeth but seemed more interested in getting us to sign a contract right away.
Remember, you don't have opinions from two orthodontists right now -- you have an orthodontist's opinion and a dentist's opinion and that's not the same thing.