If the law in your state is that you need a brake control, then they can't let you leave without a brake control. You could have walked it down the street or had a friend pick it up.
How long did it take you to get the brake control installed? Did you keep the dealer updated on when you were going to pick up the trailer?
-- if you read your contract, there is definitely fine print that says they have the right to sell it, if it's not picked up after X days (3, 7, 30, etc)
"They handed me a check for my money back (which I'm having trouble cashing) and said there's nothing they could do for me"
If you aren't financially mature enough to have a bank account, where you can deposit the check (it clears and shows up in your account), you have ZERO business buying a RV.
-- start learning money management before wasting your money on toys!
-- thankfully, the dealer protected you from yourself.