That sounds extremely hard OP. I have one with ASD but not PDA so these are things I would try or that worked with mine but he wasn't nearly as challenging so may not all be helpful.
Do the two kids have separate rooms? I would do whatever I could to make that happen if they don't already because your eldest really, really needs his own space and coming home and being alone for a while might really help him.
I would meet him at school every day with a drink in one hand and breadsticks in the other. If you come home in the car then i would have a story playing of whatever tv show he likes for him to listen to in the car while eating bread sticks.
I would avoid asking any questions or talking about anything that needs to be done when you get home. When you get home I would let him decompress in his room alone for as long as he liked and not ask anything of him - I'd actually even consider putting a little table and chair in there so he can eat dinner alone in there if he wants.
I would have his room as set up for what works for him as much as possible - lots of lights or very low light, maybe a tent bed, weighted blanket, bean bag, things he can chew on/chew toys, maybe a blow up punch bag - obviously you can't just go out and buy them all but they're things i would consider for birthday's/Christmas if appropriate.
I would have as much of a routine as possible as I could everyday so he knew what to expect. Every morning have as much set out and ready to go as you can so that you don't have to ask him to do anything. So instead of 'you need to go and get dressed now' you can say 'did you see that I put all your clothes out on the chair ready for you'.
You could put his breakfast out on his table in his room so you don't have to tell him to come down for breakfast - anything that might make his and so your life easier. If you don't have a little table then maybe a lap tray could work.
I would also try to spend a set amount of time at the same time every day doing something 121 with him. You more of a bond he has with you the more he will want to please you. Have that as a routine every day at 4:30 or whatever half an hour where you do something together, then half an hour with your other child (unless they are able to do something together with you).
At first let him choose what you're going to play, let him control it, let him make up the rules - just join in with his game in any way he wants you to. If he wants to race cars round his room with you do that, if he wants to build train tracks do that, if he wants to make towers out of blocks and knock them over do that, if he wants to play dinosaurs do that. Then you can slowly start adding your input, suggesting things to do together or things you could add into his game - but if he says no then that's fine. It's really about building connection and having fun with each other .
If you need him to do something then I would always say give him lots of warning before any transition. I used to do a 10 minute, 5 minute and 2 minute warning sometimes. Just having that time to finish what he was doing and get his head in the right space to do something else was really helpful for ds.
I really think professional advice is a great idea though - you are certainly not unreasonable to ask for it! There should be so much more freely available - we got offered a badly photocopied book list when DS was diagnosed! I wonder if it's also worth asking his teacher that has a good bond with him if she has any strategies that she finds help with him? She might have some ideas. I also think an NVR course sounds like a really good idea.
I hope things improve for you soon.