My son's hitting coach is widely thought to be one of the very best hitting coaches in our entire area. He has coached tons of college prospects, including many of the best players on many of the best teams in our area. His college guys often come to take swings with him when they are on break. Sometimes, a pro guy (mostly minor leaguers, it seems) he worked with during their youth/hs/college days stops by to chat, when they happen to be around. We've met some really accomplished hitters in passing during my sons sessions over the years.
I give that background just to frame what I am about to say. No way my son would listen to his HS coach (or even his travel coach) over this guy, if there was a conflict.
The hitting coach is also pretty blunt about which HS coaches in the area know something about hitting and which don't. He thinks certain guys know their stuff and others hardly at all. So that has helped us to calibrate a bit.
Not knowing the relative merits of either your HS coach or your hitting coach when it comes to hitting instruction, my advice is to find that one knowledgeable voice that you absolutely trust and respect -- listen to it and then drown out all the rest. (It could be either guy in your situation for all you've said. And maybe they both do, but have a different way of communicating.)
Sometimes you have to pretend to listen to the others, If it's your actual HS or travel coach we're talking about, never ever openly revolt. Never ever be disrespectful. But do find a way to seem to listen, while staying within your own trusted program.