ND kids are hard, I hear you...but at the same time I think you need to ask yourself if you are really being fair here.
I have two children aged 11 and 8 (and a DH) with ADHD and a 4 year old. The 8 year old has a very severe presentation that came close to taking him out of mainstream education until he was rescued by medication at 5.5. I work part-time (school hours). DH works full-time. So speaking from experience...
You can claim DLA for children before diagnosis if there are significant enough problems that a nursery/pre-school setting has picked up on and will write a supporting letter for. The threshold for DLA for children is that they require more assistance than the average child of the same age. So claim this asap to help with family finances and the cost of private assessment.
Kids with ADHD and other ND often need more time at preschool, not less, to settle in and become accustomed to routines, and for staff to learn how to best help them/get the best out of them. If the staff are working with you and getting to know your child's needs, you should really be moving toward the full 30 hours at this point. The vast, vast majority of kids with ADHD are in mainstream education, full time with support plans and adaptations in place. The sooner you start moving toward this, the better.
If drop offs are hard, this may not be ADHD but attachment issues, which is a whole different issue, but worth considering. (And still a good reason to aim for the 30 hours).
You cannot live in a family home and save all the household tasks for when the child is out. This is utterly unsustainable. It's good for them to see you go about normal day to day routines. Everything is educational at this stage. In fact, running around the house with you from task to task is a pretty good way to keep a child with ADHD busy. OK, it wont always be possible. Some days are just tough. But the more you do it, the better you'll both get at making this work. You might find the odd task that utilises ADHD hyperfocus and keeps them busy for 60-90 mins (model making clay playdoh type stuff works in my house) while you just get shit done. Shopping can be trickier. On-line after bed time is how I get it done, even if that's been on my phone sitting in bed with a child. Honestly, you'll hold on to your own sanity for longer if you get the housework done while your child is there and actually RELAX from time to time when they are out.
There is no way I could expect my DH to work full-time and then do solo child care in the evening while I worked. ADHD kids are hard work all the time, and tend to have delayed sleep initiation. Evenings need a joint effort. (Big respect to everyone doing this as a single parent).
This is our routine: I work 9 to 1pm. DH works 9.30 to 5.30. His late start allows him to do school drop off after ADHD meds have kicked in for the kids rather than struggling through breakfast club. I finish work at 1pm and have a bit of 50/50 chilling out/errands until picking up kids at 3pm (again, meds wear off so no afterschool club possible). Between pick up and dinner I do housework with and around the kids. We do the dinner, bed, bath routine together. At weekends we try to make sure that both of us gets some time to ourselves.
Reading your posts @Tellmewhenthegoodstuffstarts it sounds a little like you have an ideal standard (a high standard?) for the time you spend with your child. I wonder if you are bargaining a bit here (if I do x, y, z, she'll be better/not struggle/not have ADHD)? I really don't want to be presumptuous but a lot of parents who have kids with SEN/ASN experience this -misplaced guilt, bargaining, a need to control everything and "make it all better"...Honestly, what most kids with ADHD need is the minimisation of unexpected stimulation/over stimulation, and regular routines whether that is the routine of watching/helping you at home or attending preschool at regular times.