My Sun Conure Paulie will now let me take him off his cage and sit on the couch with him. He will even get on my finger and preen me. But as soon as my wife or one if my children approach, he will bite the blood out of me. Why is he doing that? Sometimes while preening me he will bite too hard but I don't think he means to hurt me. But I think in the other situation he is really trying to hurt me for some reason. I tell them to back off and when they do, things go back to normal.

How old is Paulie? The first thought that popped into my head was puberty.

Here is a link that may help you with the biting issues Paulie has.
Sun Conures, Common Problems and Solutions to Them | Birdtricks.com

I believe it's the old.".If you can't bite who you want bite who you can)..

From my understanding if she is bonded to you and some other suitor who she perceives as a threat comes by..She will bite you so you will leave the area..

It's the way it was explained to me...

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It's called misplaced aggression and it's exactly what Greenwing said.
Your supposed to flee with her when the others come around.

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Paulie is going on 5 months.

My Sun Conure Paulie will now let me take him off his cage and sit on the couch with him.
Sounds like he may need some step up training from his cage using positive reinforcement.

He will even get on my finger and preen me. But as soon as my wife or one if my children approach, he will bite the blood out of me. Why is he doing that?
Possible misplaced aggression. Does he enjoy being handled by the rest of the family? Could they be startling him? Could they be wearing something he's afraid of? More socialization and figuring out what sets him off may help.

Sometimes while preening me he will bite too hard but I don't think he means to hurt me.
He's being curious. It's what birds do. It may help to ensure that he has something to play with while he's with you. Foot toys, leather strips, wooden beads, etc. Bottle caps are a favorite of my conure! In short, redirect his behavior towards more appropriate things.

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The Earth is not flat and the Sun does not revolve around the Earth. Don't be afraid to question what you learn. In doing so, you may discover a greater truth. ~Mc

Unfortunately I had Georgie in a bad habit of biting me when "strangers" were around when she was young. It was my fault really, because i was ignorantly trying to make her be friendly and social but i was pushing her too hard. I used to take her out and pass her to people she didn't know, or put her on their shoulder. Ultimately she started to bite ME when strangers came because of what she knew i would end up doing to her. I didn't pick up on it immediately but once i did, we resolved it in time.
So what MonicaMc said is very true--figure out what sets him off. That will be key in resolving it. That's what finally worked with Georgie, when i realized that i was creating the situation that made her bite me, without knowing i was.