OP, you realise that you are being unreasonable but for your own sake you either need to make peace with the way things are (they won't, and shouldn't, change) or you should get out. 6 months is not a long time in a relationship at all, certainly not long enough for you to be dictating anything to do with their arrangements concerning children. 1 year is not a long time for the ex to have completely recovered from the breakdown of the marriage, or for the children either. I appreciate that in some circumstances this might be true but I don't think they are the most likely of situations.
I think I sympathise with the ex because I am in a similar profession, having had my DC all week and my DH being away I've got absolutely no work done at all. It's impossible to give it the time and attention it requires when you are running around after your own. Yes, she has 2 weeks off but I strongly recommend that if you are to stay in this relationship you gain some understanding of what teaching is like as a career. I think the children she teaches deserve a little more than the half effort of planning and marking done whilst being preoccupied with her own children - I'm sure if she was your children's teacher you'd have something to say about sub standard marking and planning - this is why she is upset! Look at the pressures, and the reality of her job!
I cannot understand for the life of me why you would use the phrase bag herself some free childcare! It's not childcare, he's their father - it should be free, they are his! You have made yourself sound vile with that one and have given no thought at all to her career or situation. Obviously I don't know anything about the ex's finances but I don't know any teachers who can manage on their one salary alone. Again, get some understanding of teachers' pay and conditions - you seem to be relying on the stereotype that should no longer exist. You say she is sitting pretty, but how can this be when she used to have 2 incomes and now she has one with children to raise and childcare to pay for? Surely, you can see that this is not as straight forward as that?
It's unfortunate that your DP has had to sacrifice some of his salary this month, but he made an arrangement that he had no right to cancel. If his career doesn't work around his situation then he needs to address this, he chose to walk out on his family so therefore he needs to take the consequences. He didn't have to leave with nothing, he could have arranged a fair split of assets so he cannot now use this as an excuse to do whatever the hell he likes, and neither should you.
He chooses to spend time with his ex, he chooses to stay there until after the children are in bed. You need to look at that rather than blaming the ex. Just because your ex is unreliable doesn't mean that he should be and to me it sounds like he isn't actually ready to be in another relationship, let alone one with the pressure that your relationship seems to carry with it.