Do you want support to tell your DH not to travel at short notice or any notice? Only you know how bad that would be for the job security/financial recompense he gets and what wealth & job security you want. We can't say for you. You haven't said he's generally useless.
You can make your life easier when she does visit.
Another bed to change
can she not make & strip her own bed & put the linens in machine & run the machine, and maybe even stick around when finished washing to put them away? Is the effort of finding sheets for her very annoying?
More consideration about what to cook for dinner
I presume you don't like her cooking... if swapping from your DH to a different person makes the meal planning stressful, that's another sign you're just crazy stretched too thin. ps: why can't your teens cook an evening meal for everyone?
The house needs to be kept tidier
Why?
Polite conversation to make in the evening when I’m tired and monosyllabic
So is OP working 70 hours this week, or is she having a well-needed week off? Bcz if I did all that stuff OP describes and worked 70 hours, there would be no time for anything (else) but chores, sleep, eating, bathing. No sitting still for conversation, constant movement and tasks. Constant movement and if I needed email admin time in quiet, probably would sit in bed with laptop & door closed. Besides, most people just want to be heard. It's really easy to encourage other ppl to fill silence with their own babble. Or maybe OP isn't working 70 hrs this week.
She is here for the whole week…
That's good, the bed only needs changing once, max, and she can do it herself.
DH ... Needed a “lie in”
I'd want that, too. What have you organised with him to sometimes get yourself a lie in?
whilst I got up again at 6am, did packed lunches
Not clear why teens can't do their own pack ups. Besides, it's a 10 minute job (max) if you have 4 kids (I did). If 10 minutes is so stressful to find on a single morning, you're stretched too thin.
, and took two kids to exams and work experience on 6 hours sleep myself.
I'm amazed if you ever get > 6 hrs if working 70 hrs/week. Have you considered moving somewhere (like market town in a rural county, where I lived) which does have lots of transport options from 5am-midnight? then your teens could cycle or take the many transport options.
Regular school buses (and trains) still ran every day when my teens had GCSEs, they went to school (& came home) at their usual school times regardless of exam times. Is their usual-not-you transport an option for your teens?
so now frazzled and pissed off. The mental load is large.
Mental load made unberarable by Finding sheets, making packups, mindless conversation in evenings, 30 seconds consideration of how to feed a person who is not your H... ok and some driving which you could have kicked your H out of bed to make him do, but we can't make him do that for you.
Hun, you are way stretched too thin. At least some of it is self-imposed unrealistic expectations ("house tidier", not kicking him out to drive the kids places). Gotta be realistic.