I think he's behaving unacceptably.
His behaviour isn't uncommon. Sadly. Basically, there is a power imbalance in your relationship: you are limited in your capacity to move freely, go out on a him, etc. because of the children - you are far too responsible to just walk out and leave them, and, bceause you are physically there with them, it slides into you being responsible for fixing childcare for when you are not there and, from that, to all the time with the children being your responsibility unless otherwise negotiated and stated in advance.
also there is a financial imbalance. your work at home is not visibly waged. In our current society it thus can become invisible - you're not working! (so strange, that, because I'll bet it bloody feels like work) - and the family income appears to come solely from his work.
All of this is crap. Men gain hugely from having children. They gain the respect of their peers (probably shouldn't be this way - but it certainly seems to be so) in a way that women just don't. They are perceived as trustworthy and responsible () - and all this often translates into promotions and business deals and increase in status and income.
They also gain a stability and base of affection (from partner and children) which is, ironically, often facilitated by the woman's work. Again, this has benefits in terms of wealth, health and confidence.
given all this, it is utterly bizarre that some men will still, instead of acknowledging that this is a partnership, with many benefits, and something to put work into cherishing and protecting will, instead, rfer back to veryold-fashioned conceptions of what marriage and partenrships are, and exploit the potential power imbalances.
I have a theory about this: we tend to privatise that relatinship between man and woman. It becomes up to the woman to stop that exploitation. She's supposed to get tough with Mr. Entitled, rustle up some challenges to his behaviour. Or leave.
And, of course, this may work.
But ... I reckon that when Mr. Entitled starts exploiting the differences between himself and his partner, he is actually covertly referring to wider social models - to nasty old-fashioned discourses about what a man has rights to as "Head of the family". And he is referring to wider society, in which it can be hard to be a woman raising children on her own (the thing that can stop a woman resorting to the Ultimate Sanction at the first sign of Crap Behaviour) - which can involve cultural sanctions (Did the woman leave for a good enough reason; is a woman desirable after having had children; women's lesser earning power; and more).
given this, I don't think it is just a question of the individual woman dealing with her partner. I think there is a whole question about why it is that more people don't actually step in and tell the man to pull his socks up.
Why is that?
I do think that mn is quite rare in being one of the places you really will hear that this sort of behaviour is unacceptable.
It's a guess, but OP, the fact that you are not sure if it's OK or not says a lot about what you see and hear around you.
As for what to do .... Well, given that your friends, families and acquaintance are probably not going to take your dh to one side, I guess you are left with the individual approach. We on here can tell you that he's not treating you with enough equality and respect. Will that build your confidence?
After that, you probably are left with challenging him. for that , you will need confidence, and belief that you have the right to better. You do have the right to better.