I have 4 special needs kids - all autistic and one also ADHD.
I think that the best thing you can probably do for your family is to educate everyone as to the needs and differences of the children who need the most help, and who will most likely be confusing or disruptive to your other 2 kids. Rats are born with empathy and will actually help out other rats in the lab - humans are extremely empathetic beings, and very social and kind when given the opportunity. I think that you could all learn about each other, and then things would go more smoothly. For instance, instead of seeing behaviour as annoying, disruptive, or embarassing, be sure to talk about it and see it as a need from that child, as something they need help with and deserve empathy and sympathy for. This kind of attitude will very easily flow through to your children.
I also dealt with giving up work and seriously postponing or possibly just ending my studies. My initial plan was to finish uni when my children were school age - I later decided on homeschooling, and with the different needs it will now not be possible for me to finish the degree I wanted to complete. I am now a writer, but my ability to commit is sporadic and up and down, depending on the kids and how I am handling it all.
I see it all as a new challenge, a new goal, and a new thing to get good at and give my all to. I am making a lot of progress in learning about my kids and what they need, and I am proud of what I am providing them after my efforts. It sometimes is quite boring, frustrating, and constricting due to the lack of freedom, even to go out with the kids or visit friends, but this is new and I know that my routines will change, and my life around it. I just need to make a new life, that is not the one I had originally planned and not the one I was living a couple of years ago - but one that will be great.
We don't attend any appointments apart from ones linked to the assessments and ongoing eligibility to for funding etc checks. So I don't know much how to advise you on that. You can probably get therapists to come to your home though, and perhaps they can work one on one with your child in that instance without you present. Although you can learn from therapists, there is only so much you would be able to apply in your everyday life with other young kids, and you can always focus on those things when your kids are older.
You can also consider receiving Carer Payment and using the funds for an AuPair or in home help. That would take off a lot of the pressure and you could spend more relaxed time with the kids and have someone around to help you with cleaning and cooking. I don't know what your situation currently, in terms of finances, however you and your partner could both stay home, if you were willing to both receive disability carer benefits. Money would not be plentiful, however that way you could give your kids more of your time and there would be more chance to manage everything with each of them. Since you have younger kids, either you or your partner can receive Carer Payment and the other partner can receive Parenting Payment - or you may both be able to receive Carer Payment.
I never stop doing things, pretty much all day long - that's how I am able to get to everyone's needs. That's just me though, and I have ADHD, so I don't know how it would work for everyone else. It probably just isn't possible to be always on the go for most people. Your kids will grow and then they will change and things will probably be easier in the future. Make sure you give yourself time to rest, and time to not be having a good day sometimes/often! You don't have to do everything, and if you need a day to relax with your kids then take it and leave other jobs as less important.
ADHD is manageable by keeping them occupied (if unmedicated). I do not expect my son to be able to do things like pack up all his toys, or concentrate through a new shop. I try to always factor in that he will be him, and that way I do not expect too much of him and do not get stressed when he cannot do something my other kids can do. If your son is medicated, then he will probably become extremely calm, and you will probably find things much easier in that case.
In regards to your other children; just make sure you keep communicating with them, so that you will know if they need you more. There are a lot of hours in a day, and with good planning, you may be able to come up with a family routine to factor in everyone's needs (including your own!).