Yes, Rush is always right, but, part of the problem with him not being able to play well with others is his excessive arrogance, secrecy and lack of patience. Even if someone was able to keep up with him theory-wise, he often starts in the middle, expecting people to be as up to date as he is
To be fair, he mellowed out a lot once he got over his wife's death while using the chair. That said, I don't think he and Col. Young ever had a good professional relationship while at Icarus Base, so it's not surprising that Rush didn't play well with the rest of the crew at first. Their "Rush is an asshole, so let's be an asshole back at him" attitude didn't help either.
This brings up an interesting point - did no one
in the upper echelons of Icarus Base know about Rush's wife being dead? Because you would think Wray would bring it up in discussion with Young or something in order to get these guys working together better. I'd assume marital status would be in the background information that Young and Wray would have access to given their positions (given security concerns and what not), but I don't think anyone aside from Amanda Perry knew Rush was a widower.
And really why should Young trust him after he made the decision to dial the 9nth chevron when they could have all trotted off to some other planet the Hammond could have eventually rescued them from? He's started his relationship with these people as a loose cannon and they aren't going to forget it.
I mentioned this earlier, but there's a decent chance they would've been more screwed if they hadn't used the 9th chevron address due to Stargate technobabble/continuity.
Anyway, regarding the trust issue, there should be a little trust after Rush correctly diagnoses the air scrubber issue and manages to keep some idiots from killing his entire team (although two people do manage to get themselves killed and Franklin had to be shot). At the very least, I would trust that he knows what he's taking about when it comes to the ship and tech, especially when my second best scientist is a complete rookie with next to no knowledge of SG physics/tech at all. Sure, he might not have the purest motives, but I'd at least trust that he's not going to screw over everyone else out of a sense of self-preservation.
Then again, Young seemed to be really paranoid when it came to Rush in S1. At the end of Light, he jumps to the conclusion that Rush knew they'd survive, when the facts all pointed to them probably dying by flying into a star. At worst, Rush didn't tell them that the ship might
refuel by flying into suns, which is totally reasonable when dealing with a ship that they couldn't control, had no power, and was so old that the air scrubber broke five minutes after they arrived. At that point, I would've assumed death was imminent too.