Bless you, I'm so sorry that sounds really hard.
While not as difficult as your situation, I can empathise as my middle son is very coffin my other 2 children, and navigating family life with him can be so hard and tiring. By the end of today unwound have spent about 18 of the last 72 hours at the park.
I don't have much practical advice especially as my son has no diagnosis and I do have a partner so I can split the children up as needed, but one thing I will say is contingency, contingency, contingency.
I lug a boatload of stuff out with me in order to mitigate/premempt as many deviations to a peaceful day as possible. Screens, food, toys, fidgets, spare clothes, etc. Escape routes and planned diversions thought of ahead of time.
Are there any ways to plan events your DC like going to that would allow you to cope with and be allowed to leave the younger DC to do their thing? Are their soothing items you could bring your DD you wouldn't normally want to bring out? I'm thinking in a festival setting, is there an accessible/sensory area or empty/fringe space you could go to while your DD blows over?
Sending solidarity and sorry for the poor advice; I do know how hard it can be to have a DC who takes so much more parental input than others.