I agree with PP - the school sounds awful and you need to leave.
You'll still have to do parents' evenings at other schools, and not be able to see your children on those evenings, but that's par for the course for a lot of jobs, teaching or not.
It's not the parents' evenings that are the problem, it's all the other stuff, and the fact that they've timetabled other meetings etc in the same week as parents' evenings. You're being massively overworked, and the stress of that is taking its toll on you.
I worked in a school for 2 terms, then left because it was shit (and not as bad as what you're describing). I then worked at another school, also for 2 terms, and again left, because that was also shit (still not as bad as you're describing. While I was at the second school, a job came up in a lovely school that I'd done supply in (bog standard state school, but lovely kids and very well-managed), so I took a job there, and I'm happily settled at this school now.
Lots of schools are shit, they don't deserve good teachers, so try to get a job in another school.
There's no harm in applying - the schools you apply to will decide whether your CV is a bit dodgy, and you've no idea how dodgy everyone else's CV is - a lot of teachers move around these days due to the appalling management in a lot of schools. You never know, the school you're currently in might be well-known amongst head teachers as being a horrible place to work.