After reading alot of the comments you've made OP, it sounds like you're the issue here.
If you didn't want this extra responsibility, then why get with someone who already has children?
You should have got with someone who was childless before you.
It's not their problem that you two decided to have more children.
That's your issue.
You decided to make two more children, on top of the two already here.
That was your decision.
So work is tough at the moment.
Everybody has that from time to time.
They're both high school age, so it's much less hassle than dealing with babies & toddlers.
They'll just entertain themselves.
It's not that you can't, it's that you don't want to.
Which, is entirely you're right - if that's how you feel.
But remember, actions like this have consequences.
Most men would never forgive this.
So you could well be starting the end of your own marriage.
And then there's the children themselves.
They're going to be aware of how you feel.
So don't be bleating about lack of invites to their future important days, such as their graduations, special birthdays, weddings & christenings etc.
Maybe their Mum just wants them to have their usual routine.
Alot of children act up really badly, when this is disturbed.
Routine is often a child's safety net.
So perhaps it actually has nothing to do with being awkward at all.
Plus, maybe they want to see/ spend time with their siblings.
With seemingly no set end date to this change, just exactly how long do you expect everyone else to juggle around you?
They'll be in bed anyway.
And running around dropping off at holiday club, is what you signed up for when you married a man with two children.
If you still feel the same, then maybe you don't want to be a part of this family unit & perhaps it's time for an honest conversation with your husband about divorce.
You're supposed to be a team.
Working together & having each others backs.
Making hard times a bit easier for each other.
But if you're not willing to do that for him, is he really the man for you?
I'm sure your refusal will have him asking similar questions.
I'd say good luck.
But tbh, I don't care about your feelings - you're an adult.
I just hope you don't manage to cause an issue with him and his children's relationship.
And I hope they're not emotionally or mentally effected knowing how you felt & treated them.