As a temporary measure, can you or your DS sleep downstairs on an airbed with your DH/partner for a while? So he can get some sleep and you can be up with your daughter without disturbing anyone, make it into an adventure, even put a tent up in the living room - I think once he's had some proper sleep you can start to go back to his room and the tiredness will be much more subdued.
How about some ear plugs or eye covers for your DS, block out the sound and light for him?
I have 2 boys, 5 years apart and I used to leave youngest in the cot and do 20 mns half and hour with my eldest to get him calm and ready for bed, even if my youngest objected it was tough. He soon learned just to entertain himself for that short time, then I would leave the eldest in his room, with a book, some soothing classical music and shut the door, then go and put the younger one to bed, story lights out etc, then got back onto the eldest room, read to him, stroke his hair, cover his bed in lavendar oil, leave a night light on and shut the door.
Also, very hard to do, but if I remained calm, did not shout or get stressed, the better is was. Get your son some dedcent sleep, then address you 1 yo sleep eg: staying with her til she's asleep, then you will all have better sleep and be happier.