Hello Writing.
You've explained yourself well. It seems you don't tolerate your partners children as comfortably as their dad does, and you're not able to control them or mold them the way you have your girls so far. You admire the gorgeous man and love the boys, but there are other influences on his boys, and they swear. If you lived together, some rough habits will rub off on the girls. This all seems true.
My experience is that to enter into a living together arrangement, you do have to prepare yourself for compromise. Push yourself, see the upsides and not just get irritated by the negative. Unfortunately, there is no place for your jealousy of two little boys, and this persists into the boys 20's. It will be one of your petit character points to work on..and I am sure your partner will have little irks that he has to cope with.
If you live together there would be upsides. Your girls will learn that mummy is loved and respected etc etc and they will see how a loving relationship looks. Also your man is a teacher, and so is presumably especially skilled with children. The sort of roughness of the boys is seen by your girls at school anyway.
FWIW mine were young when we got together and I have faced these issues. Nevertheless, I dont regret it, and although a compromise, I still see glimmers of the integrity of my upbringing for MY children, and I have brought a little more affection (and polish) to my step children, that they otherwise wouldn't have had. And I accept that i have lost some ground too: my children's work ethic lessened perhaps, and attitude to bedtime and computer time, and snacks. But maybe, I would have lost some of this ground anyway. My DH boys were chubby and pale when I met them and I was able to improve this for them. It was a symptom of a failed marriage and absent mum... the boys were latch key kids with a working Dad, who was doing his best. They played outside with us more, wanted to be with my children more and more, and now blended, there are far fewer differences. Focusing on the positive is a really good thing. And being remarried and happily married is easier and more soothing than being alone (but not as much fun, nor as independent, as the dating era was!!)
I can't sprinkle fairytale dust for your future, though I wish I could. If you live with this man and take on a role of step mum, the man has to be fabulous in your eyes, treat you with respect (cant teachers be bossy?) and you have to be ready. It is a relentless, tricky role being a SM and it will alter your family dynamic and your girls will lose something, and gain a new aspect. But life changes anyway. Nothing stays the same. Any period of courtship leads to change as it is not a static state.
Well done you seeking advice. There is a lot to think about and to get into perspective. Indeed, I maintain that step daughters can be trickier on average than step sons (I count myself lucky not to have stepdaughters).
Can you keep going financially, separately, for both young'uns to start school. That brings quite a change. Will it be the same school?
Will your ex's cause conflict if you get together?