You need contingency plans. I know that you presumably manage everything yourself in the way you've always done them, but as you've found today, sometimes shit gets in the way.
- Tutor. At 14, DC is perfectly old enough to catch a train to Clapham, one to Raynes Park and make their own way from there to the tutor. Planning the route in advance would make it something that could be done at short notice (I understand doing it for the first time with no notice isn't feasible).
- Exam revision. It's good to have a day off, as it allows anything that's been covered in the last week to sink in. If they don't know it by now, forcing them to do more will help neither memory nor stress levels. This applies to both external exams and end of year tests - it also teaches DC that it's not obligatory to be active and doing something all the time, that rest is also an important part of getting things done, like it is essential for training/exercise; overtraining the brain is as much of a problem as overtraining the body.
- Animals. They'll be fine in an upstairs room for a while (bathroom?). Having a spare litter tray so you aren't lugging an existing one upstairs, along with one of those Sanicat twin packs of litter tray inserts and a bin bag will make relocating and cleaning up after them easier. Chuck a couple of big towels/a dressing gown in a heap in the corner will give them somewhere cosy to snuggle up.
- Parties/Social engagements. Sometimes they have to be missed if there isn't somebody else who could do you a favour if asked.
- Workmen. If something is booked by either of you, it is accompanied by an A4 sheet saying exactly what they are coming to do. No excuses (looking at your DP here). Makes it easier for them as well as you, as there's no confusion about what is needed - and giant DC can deal with it without worry, thus freeing you slightly.
What is most obvious to me, though, is that you need to get used to asking for help and delegating. I'd have refused to move wheels, whatever footwear I had on (I usually have trainers or steel toe capped boots on at work and I still wouldn't attempt it). Either they come and get the things from your car or they don't get the business/DH has to sort it out instead (my preferred option, personally, but sometimes it's good to be supportive).
If DP wants to book work, he writes the A4 sheet of requirements first. It means you won't get caught out paying for work that wasn't included or they get paid for 3 jobs when the price agreed was for 5 (and vice versa/getting the eldest to help out - 'do you want us to - ?' 'It's not on the sheet Mum/Dad left').
I wonder whether you hold all these tasks in your head? Having a planning board, say, on the fridge door, helps, as everybody can see what is needed. Rather than a vertical linear structure (a list), something more like a branch and stem might help - so they're in chronological order, but a stem comes off with the separate elements and who is doing them/details goes there. Use large writing/marker pen size, so it can be seen at a glance. It also means that anybody thinking 'Oh, it's not much to do, I'll just add that on' can see that, actually, the day is already crammed full of things to sort out. And make a point of scheduling 'RELAX!' in there. It's important for everybody - scheduling it makes this clear.
I used to hold everything in my head - I did it at work and at home, but that meant that if I was caught out by illness/emergency, nobody knew what was going on and the workload increased until I felt constantly under pressure and frantically juggling things in my head. Putting the list of things I needed to do, what factors were influencing it, who I was dependent upon to complete them, what other help I needed, etc, into a very visual format made my boss realise that 'Can you deal with this?' wasn't always as simple as they thought - they could come in with another idea or task that sounded simple but never was, look at my board and think maybe it wasn't quite as urgent or important compared to the 55 other things already on there. And I didn't get asked 'why haven't you done this yet?', as they could see at a glance I was waiting for a reply from somebody else.
Perhaps doing that could mean when DH comes up with another thing to do whilst he's away/out, you could direct him to the board where he could show you exactly where it can be fitted in? (Either nicely 'Let's have a look' or not, whatever works for you/your mood).