One thing you can do is hitch up as set to tow. Pull the e-brake pin and see if the brakes lock. If they don't, that is the first problem to solve. Pulling the pin sets the full battery amperage to the brakes--should not be able to move the trailer. After checking this, replace the pin soon as possible, not good to leave that amperage on those small wires.
There are very few places that I have known who could get these type problems solved--GM dealer will say its the trailer; RV shop will say its the controller; and you still don't have good brakes.
Does the new trailer have disc brakes?
I had a friend with a '15 GMC 3500 who never could get the brakes to apply correctly to his HitchHiker. Replaced the controller twice by GM, still no good. Before he got it fixed, traded for a MH.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired