I help coach my son's team as well. It is a hard balance but it can be done.
At 12 they still have a lot of developing to do and while my son's team is only a year age wise ahead of yours (we are practically neighbors by the way) you begin to see the seperation. Some kids don't throw any harder now than they did at ten. Some kids can't get the feel for anything other than fastball or fastball doesn't move. Lots of reasons why they may not pitch anymore.
Conversely don't assume that hitting now computes to hitting later. We have a couple of kids who tear up average and below pitching but can't some close to anything with plus velocity. Guess what as you get older the bad pitchers stop throwing.
Unfortunately mine is wildly erratic at the plate. Will hit .400 for three months, but then won't strike out but will ground out to short three straight tourneys. So every time I go to pull the plug on pitching he stops hitting for a month and gives me pause
I know with the pitching he can still contribute to a high level team during the times he is struggling with his stick.
My experience is yes manage it, but don't walk away from the pitching just yet. If you can't work it out with this coach find one you can in the future. If he is catching more than 50% of your team's innings at this age find another team with a solid catcher, because even without the pitching at this age he needs to be somewhere else for his body's sake. Mine wanted to be back there all the time. He now welcomes his innings at first base as a pleasant break physically and mentally.