Fellow HOD and union rep who has working in a school in SM and also RI. Advice at the bottom of my post.
50 hours per fortnight should produce 5 hours PPA.
You cannot be directed in your PPA - i.e. told what to do with it. However, you can be delegated tasks for your gained time.
If I understand you correctly, you have 4 x HOD management hours per fortnight (same as me). Like you, one week 1 hour is taken up by an LM meeting, the other week 1 hour is taken up by LWs.
5 + 4 = 9. Therefore, timetabled hours should be 41. I get 2 additional hours per fortnight compared to you for departmental meetings - meaning I have 39 timetabled teaching hours over 2 weeks.
Re: briefings, CPD and meetings; assuming you're on MPS and your school follows the Burgundy Book, these should form part of your 1265 directed time, along with progress evenings, etc. If you're on Leadership, then you're not covered by 1265. Morning breaks, technically, we can be directed during those to do duty as they're paid but, crucially, these are budgeted into the 1265.
In terms of calling home, this could be considered reasonable additional hours to discharge your duties and not part of your directed time. However, management can't tell you when or how to do this.
Long story short, yeah, you're being worked too hard, especially as you're saying that you're being worked too hard. You need to speak to your union rep in the first instance. If you haven't got a competent rep at school, then you need to contact branch. If you're an MPS teacher, the first thing they'll be interested in is your direct time calendar. If you're not an MPS teacher, they'll be interested in the extent to which expectations of management match the capacity of staff. You're definitely being shafted with PPA though. You can challenge next year's timetable with your LM. You should also tell your LM that you're struggling with workload at the next available opportunity.
On a slightly more personal note, I've been in the position where we've had to turn the school around (before I was HOD) and it was tough. The members of your dept also have some responsibility. It's not necessarily up to you to do everything. Delegating is an artform. The Education Support Line is 24/7 and staffed by people who know what they're talking about. It might be that you consider reaching out to think through your position and any possibilities to improve it. It's a hard place to be, middle management. Having someone to talk to could be helpful for you.
Sorry you're going through this.