I don't get it, I don't understand. If your son wanted a trumpet and you bought a trumpet then I'd say he needs to stick with trumpet because you spent the money and he needs to stick with the responsibility.
The instrument the band director suggests is also a brass instrument just bigger. So, if he sounds bad on the trumpet, then wonder what he's gonna sound like on a bigger brass instrument.
Mom, do you require your son to practice daily? A private instructor can only show what needs to be done and how to do it. It's up to the parents to be sure the kids practice.
If the son isn't up to par then why? Find out what is needed to get him up to par and this is what the private instructor needs to work on.
I'd listen to TrumpetMD