I can relate! I wasn't a HT but deputy in a very large international school, we don't live in the UK. DH also had to travel every quarter. Due to where we lived a 7 day work trip would be 10 days because of travel. I also have 2 children and also similar to you, i was the main wage earner as even though DH had a good job, he was remote, so his earnings were on a UK scale but we lived in Scandinavia. We definitely couldn't afford to outsource!
My tips are
Get out of bed AT LEAST an hour before everyone else. I used this time to have a coffee, check my emails (so I knew what I was facing ahead) and get myself showered and dressed before anyone emerged. This worked wonders and I cannot recommend it enough. It did mean I woke up at 4.30am in a week day though.
Slow cooker, especially when DH was travelling. Homemade meatballs, curry etc, prepped the night before, in the fridge, put it on as you leave. When you get home, it's a quick pasta, rice, potatoes in water whilst kids have a shower and pyjamas. Then dinner together after.
Capsule wardrobe- i don't have Next here, but have a similar shop with multiples in a collection. Works perfectly.
DH and I use a Trello board for family admin. The more you use this the better it gets! No more discussing admin, missing appointments or forgetting to buy milk. I use Trello in my work now also.
Make sure you have as much electronic help as possible! Dishwasher, robot hoover, self dosing washing machine all helps a lot!
Working in schools is often impossible to switch off from. I had 2 mobiles, one for me one for work. I made it clear to my tram that after 5 30pm on a Friday, I was done and would be available again around 6pm Sunday. Phone went off.
I studied as well at one point on top of full time. During this time I often sat in bed with DH after kids had gone to bed with my laptop. We watched Sopranos and I did my paperwork. Doesn't sound ideal, but we actually look back on it fondly. DH used to provide good snacks too! It worked better than me stressed sitting at the table.
I would also suggest whispering book a day off work, one that won't cause you more work to have off and use it to set up our new admin/life routine. Get ahead. Set up Trello, order some, clothes, prep some meals etc. Give yourself the time and headspace to figure this out. 1 day will make all the difference to you, but won't matter to anyone else.
I hope this helps! But honestly, it gets better.