You really sound like you've got your hands full. I can't imagine!
To me, having 3 conures, it sounds like he's wanting attention. If he bonded as a mate with your niece and your niece is no longer there, that should not be the problem. And while I agree with your vet regarding large parrots and "inappropriate" petting, I don't agree with him / her on conures. They are pretty equal opportunity parrots.
With Doc, it sounds like there is a lot going on around him, but in his opinion, not enough attention is being directed towards him. With two young children, that isn't going to change for quite some time.
If he is unhappy and making the household miserable, have you considered giving him to the niece? Would that be an option at all?
We had an umbrella cockatoo. I had dreamed of having one my entire life. He was 6 years old when we got him - we had cockatiels and budgies before, but knew absolutely nothing about cockatoos other than that they were beautiful and entertaining. The first two weeks were a breeze, and we fell in love with him. The more used to us that he got, the more time he started spending with my husband, which was fine, but no one ever told us to only pet / scratch around their head and neck. Sucre got a full body rub down every evening when we came home from work. He started screeching anytime he wasn't on my husband. He became terribly aggressive towards me, to the point that I would have to close myself off in another room to keep from getting attacked. I sought advice and we worked for weeks trying to get him to at least accept me in the same room. When we realized how upside down he had turned our lives, we knew we had to rehome him. We had 2 little dogs that he terrorized, lovebirds and parrotlet getting absolutely NO attention, and we were working all day and spending our evenings in separate rooms to try to keep Sucre happy. We both cried for days, but it was for the best for him, and us. He is now living with a single lady who takes him everywhere with her. He's had more vacations in the past 2 months than I have had in the past 10 years. He exhibits NONE of the behavior he exhibited with us. She's had birds for years and she knows how to handle him. We did not.
I can feel your frustration in your posts. Doc can certainly feel it in the same room with you, just like our U2 could feel my fear. You can't control how you feel, but you can do what you have to do to make everyone's life easier.
I don't advocate rehoming animals. In fact, I do small animal rescue. But I do believe that with birds, sometimes you just don't have a good fit, and that really sounds like the case with Doc. Your plate is just too full, and I bet the stress is affecting everyone else as much as it is you.
Good luck with whatever you decide to do. Just know that sometimes the last decision you want to make is the best decision.