So, I'm hearing you list several things you *do* want...
You want to have family dinner time together (if not every night, then X nights per week).
You want family time together in the evenings (but your tutoring also interferes with that?) Sounds like you think your tutoring is higher priority but he may not be on the same page with that.
You want the kids to be in bed at a regular hour so they're functioning better the next day.
Can you see that (even aside from the issue of female attention) that H may be getting some satisfaction from teaching that he may not be getting elsewhere? Can you find a way to get your needs met while also finding a way to get his met? Would it work if he only taught 2 nights a week? Or if he found some other way to get that satisfaction that still took some time away from the family?
I'm not sure how to address the flirting aspect, exactly. I assume that you want to feel confident that that sort of attention is only directed at you. His denial/cluelessness doesn't put him in a good position to be able to address your concerns. It's worth taking some time to sort out your thoughts on this. One thing I wonder, if he's so clueless about it all, then how can he assure you that he's not going to go down the same path again? What is he changing in order to assure a different outcome when women come on to him?
Your thinking has evolved amazingly in the time you've been here. Keep chugging along and things will keep sorting themselves out.