From my own limited experience with baseball (my kid is 12) I would have to say that you as the coachhave to be consistent. Make your rules and expectations known and stick to them, regardless of the W/L.
The biggest let down I ever had (as a parent) from a coach was me telling him my 11 year old didn't turn in 3 pieces of homework in one class in one week and can you please sit him for Friday nights game so he can watch in full uniform from the bench...his response was to bargain...what about 3 innings instead of 6, I just can't afford to sit him for that long". We left that team the following year and joined a team where the coach said his number one priority was to play the best competition we could and to teach these boys how to play true baseball and we might not win a single trophy all year, but the boys will learn.
As a High School coach you are their teacher, so teach...even if it means sitting the 2 stars of the team on the same night and make it known to them WHY they are sitting..I think the rest of the team will give them a good deal of grief, and if that doesn't make them feel bad for letting down their team then you are probably better off without those players.