OP, you've gone on and on about how 13 weeks is too much time off for a manager on that salary. Except she IS working on that time - parents simply cannot contact her. It's not as if she's off on a jolly. No HT is able to get away without working in the holidays, so you can stop your sighing over how lazy you perceive this one to be just because she won't answer to parents. Not a correlation.
As a teacher, I can happily restate PPs that the issues you are demanding to discuss are not appropriate for a HT to deal with. You seem to be fairly resistant to being told you're unreasonable but I'll try to explain again.
A) Even if PTA funds could be used for staffing, no school advertises for jobs over the summer. What sort of crap candidate would you get who hasn't lined up a job for September? What a waste of funds because in case you hadn't realised, advertising for a job is costly. So that issue would have to wait until September. Except it's a non issue.
B) You cannot address behaviour issues outside of term time. This should be obvious but let's explain. Aside from the difficulty of getting all pupils involved and their parents into school - what sanction can you put in place? You can't set detentions or exclusions in the holidays? Also, these are small children, their attempts to improve their behaviour need to be done immediately - impossible to say 'right you need to be nicer to X, try again in 6 weeks when you see them'. Ridiculous.
C) class sets are done. If you had a request, it should have been made BEFORE TERM ENDED.
You are being completely unreasonable and you simply sound like you have a personal issue with the HT. You don't have a clue about how schools work and worse, nor do you care. Yes, parents are stakeholders, but that doesn't mean you just demand everything you want. Try working with the school, perhaps, starting with raising issues in term time.