I love the photo of the tiel with the chickies! SO cute!
I would not let your parrot on your shoulder if you are having any "aggression" problems at all. I agree with Anatopism that you've got to insist that it stays on your hand.
How old is your bird? Is it possible that it is going through puberty? Their behavior will often change for a year or two while this happens. If the conure is attaching itself if your boyfriend, is it possible it sees him as a mate? If so, yes, you would be seen as threatening that relationship. Your boyfriend can take steps to make sure that the relationship is that of human and bird in the bird's eyes, including not petting it on the back. Anatopism, do you know of any other ways to redefine the bond?
Does your bird know "step up"? I make sure to actually talk to my conure when I go to visit her. I say hello to her, tell her what I am doing and ask if she wants to come out and step up on my hand. I find that she responds really well to this, especially if I am super enthusiastic about it! Sometimes she puts her foot out to step up and sometimes she holds onto the side of the cage, I know when she does this she doesn't really want to come out. I try to respect that, unless by chance I have to get her out.
It's easiest to deal with birds in the morning. At night, they can tend to be grumpy.
Overall, the best advice I can think of is to go slow. You will have over 50 years with your bird, you have time to train it right and create the most positive relationship possible. Spend time in the same room with the bird, maybe with the cage door open. Talk to it. place your hands slowly around the cage. Go slow when cleaning and changing out food.
I hope these little tips help. I know I am new here, and new to chickens, but I have kept parrots for several years, and I study behavior and training all the time. I'm no pro but I'd like to think I learn as much as I can and put it to use.