Staying with someone just for the sake of the kids doesn't benefit them at all.
If you're not happy and you've tried different things to try and work out the relationship and nothing seems to work then you have to do what you think is going to benefit you and the kids.
The kids will pick up on the fact that you aren't happy and are arguing and this will reflect in their behaviour which could also be a contributing factor towards your son's behaviour...
You might find that once you are no longer living in the same house, that you get on better and that your partner treats the kids more evenly.