I'm going to agree with @EverybodyLTB - you have a huge problem with your son, and the answer is not to give in to him.
He sounds like he could be on the spectrum, BUT he is definitely an abuser, spectrum or not.
You have tried to placate him by always doing what he wants, apart from staying away for a night, and it's just made him even more demanding.
I would continue with your overnights, and also limit how often you answer his messages.
Make sure your older children have your partner's number so they can get hold of him/you in an emergency.
Your youngest son's behaviour is NOT normal, and you do not have to put up with it. If it was a partner, everyone would tell you to LTB.
If he refuses any medical or psychological help, then you can only help yourself.
I would be gradually cutting down on contact time with him the rest of the week, and encouraging him to spend more time with friends or other family. This is normal life, and will be good for him as well as you. If he cannot or will not, then you need to consider other ways of getting him the help he needs.
And you should be getting professional support for yourself eg counselling or therapy.
You also need to stop giving him control over any aspect of your life - i understand it's probably happened little by little, but it has to stop.
Your goal initially was probably reassurance of your love and that you would always be there for him.
But - read what you've written about what he controls - that's really crazy, OP. And it has created a monster.
I would continue seeing your partner as you have been, but maybe consider having him stayover maybe once a month.
Good luck, it's not going to be easy to extricate yourself from this toxic relationship with your youngest son.