Disclaimer: The Avengers do not belong to me.
Takes place after the Avengers, and Age of ULTRON never happens here.
They don't trust him. None of them. Not Natasha, not Clint, not Bruce, not Thor, not Steve, and not even Pepper. And not in the we-are-sure-you-cheat-at-cards kind of way, but in the as-far-as-we-could-throw-him-with-our-hair. They trust him to do his job somewhat haphazardly. And that's it. In battle, they always double-check everything he says because they believe he can only lie with his voice, but as they can not see his face, they don't know whether he is lying or not. They don't know that Tony is a better liar than Natasha, having fooled millions of people over the years, every year. He learned to act from his very birth, to keep up fronts fro his family and the public, so that they trust him, and don't mind him, and like him, and don't see him as a threat.
He carefully acted in a way that would make him appear as a narcissistic, eccentric genius, playboy, millionaire, philanthropist, and nothing else. 'Textbook Narcissism' indeed, as he memorised a set of behaviors that he integrated into his public personas. After all, it would not do for the media to find out that he had a low-self esteem. They'd rip him to shreds. He could not hide his genius, so he set up to fronts to deal with that: the occasionally appearing calm, cold, confident and charismatic genius inventor, and the charismatic, irresponsible playboy that he used almost all the time to make people forget the other front. In truth, he never actually took anyone to his bed after parties, but simply slipped them some sleeping pills and asked Happy to drive them home. While in his teens he had realised that he was not actually attracted to anyone, and had also realised that that was not normal, so he acted like he was, and set up situations so that people thought that he was just like them.
He created the Iron Man front after Afghanistan, to destroy his tormentors and to protect innocent people from predations of such monsters. He did it because he had the ability to do so, and would not get in trouble for delivering vigilante justice. He set things up so that the people loved him, and thus he could not be disposed of some random night. He also took up the mantle of being a hero for Yinsen, so that his sacrifice saved several people, instead of one worthless, useless murderer. He is not a better person: he just got a wake up call about how to go about protecting people. He is still pretty much the same, except he has PTSD now, and is afraid of water, and his paranoia increased. Privately, he finds it absolutely hilarious that he managed to separate 'Tony Stark' and 'Iron Man' so well that they see 'Iron Man' to be the dangerous one "take that off, what are you?", and no seems to fucking remember that he built the suit in a dirty cave while he was slowly dying, and that he was the one wearing it and controlling it, and not some other person. No one seems to realise that the Iron Man, Tony Stark, and the Genius Stark are the same person, and Tony would like it to stay that way.
There is one exception, only one person to really understand that Tony Stark, Genius Stark and Iron Man are the same person, and that is Loki, who Tony could tell does the exact same thing, and creates multiple fronts, and Tony has a nasty suspicion that Loki was not really in full control of himself during the invasion, and that the whole thing was partially a test for Thor, to see whether he would consent to working with others. Tony wishes he could have spent more time with Loki, because he wonders just how deep the similarities and parallels run between them, and because he has a feeling that one day he might trust the guy, not completely, but more than anyone else except JARVIS, if he spends enough time getting to know him.
None of the Avengers understand, after looking at his 'public' biography, why he took up the hero business. They assume it's because he got bored, so they are expecting him to turn villain. No one knows exactly what happened in Afghanistan, and no one knows anything about Yinsen, except JARVIS. He made sure of that. And he does not mind that they don't trust him, because he doe not really trust them not to betray him, either. After Obadiah he is always double-checking, always expecting deceit, and lies, and betrayal. He does not trust Steve because a guy that open must have secrets, and Steve does not trust him because he is a genius, and sarcastic, and begins each morning by telling them six impossible things before breakfast, because 'Alice in Wonderland' and 'Alice through the Looking Glass' had always been some of his favourite books. He does not trust Bruce, because Bruce is smart and Bruce is the Hulk and can pound him into dust in seconds, and Bruce does not trust Tony because Tony is a scientist, and rich, and his reach is everywhere. He does not trust Thor because he is alien, and their cultures must be incredibly different, and Thor does not trust someone who's face is often hidden by a helmet. Natasha and Clint are spies and they are SHIELD and that is enough for mutual distrust. He does not trust Pepper in the same way he does not trust a person he meets on the street, and maybe the same way he no longer trusted Obadiah after Afghanistan, and maybe he should go to a therapist about that (as well as about the nightmare of Afghanistan and the wormhole, the low self-esteem and suicidal behaviors), but Tony does not trust random people, no matter how may contracts they sign, and so he just talks to JARVIS about his problems, and JARVIS listens, and wakes him up when he has nightmares. Pepper does not trust him, because after Afghanistan she no longer recognized him, realizing that she only sees facades, and not the real thing, and because she does not know what the real thing is, she does not trust him.
He only trusts JARVIS, because he knows him better than JARVIS knows himself, because he made him, and taught him, and is his protector. He built JARVIS from nothing, created each and every base part of him, and then helped him learn, develop his own personality, become whoever he wanted, and though he knew that was dangerous he never cared, because JARVIS was his child, and he was a living being, and shutting down an innocent being or remaking it whenever it showed signs of wanting to be it's own person would be cruel, and Tony was not that cruel. And the risk paid off, because JARVIS turned out sarcastic, and kind, and loyal, and occasionally rather cunning person, and most certainly not a killer, psycho A.I.
The Avengers trust JARVIS. They don't trust Tony, because he is human, and humans are unpredictable, but they think JARVIS is simply a program, one that they can easily put down whenever they want, that Tony would shut it down for him, because if JARVIS went craze he would certainly go a after Tony - in their opinion. Tony did a better job hiding the nature of JARVIS that anybody could ever imagine, and nobody would believe him if he told them, because they do not believe him capable of that level of deception. He even made a hologram ball that supposedly showed what JARVIS's 'systems' looked like, making sure it looked mechanic, and nothing like the actual JARVIS, a hologram of whom would have taken up the entirety of any lab, that would have looked unsettling large, and organic, and complicated, and frightening to the fucking Avengers, who were paranoid and twitchy, putting down anything resembling a threat. He discusses the ULTRON project with Bruce where the others can hear him, because he wants them to believe he is not clever enough to create something like that, to throw them off the trail of JARVIS if they were on it.
They trust JARVIS, and they don't trust Tony, and they should not trust the first and should trust the second, because JARVIS is loyal only to Tony, and would do anything to protect him, and Tony would do anything to protect JARVIS, but he would also in most cases care about the others. JARVIS would not care how many he killed to protect Tony, and Tony would count each one he killed to protect JARVIS, and then send apologies to the family.
Tony lives by the maxim of "keep your friends close, and your enemies closer", and lets the Avengers into his home with a smile and a laugh, while he and JARVIS secretly analyze each and every single one of them, and design ways to deal with them quickly and efficiently should they ever need to. They have created plans for hundreds of possibilities, and still create more, because both of them are paranoid and overprotective of the other. They only trust each other, and it is enough for them.
Trust has to be earned, not freely given, and Tony doubts that he could ever trust any other person other than JARVIS, because he is too paranoid to let anyone in that closely, to see if they could be trusted with his secrets.
And so goes on, pretending to be harmless, feeling his back prickle very time he turns his back on the other Avengers who are watching him like bloody hawks, waiting for the first sign of a betrayal.