I think that this is a common issue. I find it disappointing to see people suggesting that spending money is the answer. Yes better kit will reduce the problem but the bottom line is that film sound tracks have a huge dynamic range. The sound levels are meant to be standardised for all cinemas. But this standard produces sound levels that would be unaccepatble in many living rooms.
We swapped from a hi-fi separates system to 5.1 system to help with the problem. It did and I can't see how on the same budget a stereo system would ever be better. The easiest fix is turning up the centre channel, this was never an option with stereo. I have seen movies with a sound through a really high end stereo and it did sound really good but it doesn't in any way tackle dynamic range
To be honest we have only really dealt with the issue by accepting high volume levels in action sequences. Our kids are adults so we aren't disturbing them, we don't listen late and next doors kids are teenagers as well so its not like anyone is trying to sleep through it
If the kids were younger I'd be looking at dynamic range changes in the processor. I really should get the manual out for our receiver
I hope you find a solution