Hi OP.
You are sounding very tired and unhappy.
In the OP you mention your 7 year old who is under assessment and has toileting issues/ You also mention medical appointments, and later say that a crunch point regarded him soiling himself. I could be totally wrong, but is this a major cause of stress and additional work for you? TBH, I would expect a NT 7 year old to take off the soiled PJ pants (from your other posts these seem to be disposable ones). Is DH in denial about DC7, the impact this is having on you and thinks it's all just going to go away?
One practical thing I would suggest is giving everyone in the family, even the littlest one, their own particular job to do each day. So the wee one might fold up clean tea towels and put them away, DC7 might set the table and DC10 might do the breakfast dishes. the older the child, the more they can do around the house - it's a part of family life, not just mum and dad doing everything. Things like dusting, sweeping/hovering floors, taking out recycling are chores the older two can help you with and they should keep their own rooms tidy, be responsible for putting dirty clothes in the laundry basket etc.
At night, DH would be responsible for tidying the living room each night and bringing through cups etc while you wash them up and do last tidy round kitchen. So between you, you make sure the downstairs is tidy each evening before you go to bed.
Maybe you do have to spell it out to DH: "I'm going to the shops, so when the washing finishes can you hang up the clothes, please?"
Change beds at the weekend and get DC10 to help with their bed, while you and DH do the others - it's faster with 2 people doing it.
Sorry if these are things you've already tried, or if DC7 isn't able to participate - you didn't give many details about the possible condition so I do appreciate that he may not be as able to participate.
Can you regular things as a family, rather than the separation of Dad works, Mum looks after the house? So going for a walk as a family on a Sunday afternoon and then everyone helping to make the tea together? One of my favourite treats as a child was when we had pancakes for a special tea - getting to help whisk the batter, watching as they were made and of course eating them with butter and jam!
You sound very overwhelmed, so I hope that maybe something in here might help a wee bit.