I think the scenario was pretty weak but there are some elements that explain it:
Why do they think the gorillas from Earth-2 would attack Central City ?
They were lead by future events to believe that it would happen. When Barry and Cisco vibe into the future to see the TV headlines, one of the titles is "City still recovering following gorilla attack" (2:43 of the clip), so the attack was plausible. Since the only population of intelligent gorillas they know is from Earth-2, they didn't ask more questions.
Why did they trust Grodd (of not betraying them)?
The main reason is that, at that moment they had nothing to lose: they were trapped and Grodd were offering them a way of escape. Did they trust him of not respecting his part of the contract? We don't know but from their point of view, Solovar or Grodd as a leader of Gorilla City makes no difference. If Grodd don't free them, they are in the same position as before, with the slim advantage that they know their ennemy well. Another advantage is that Grodd may keep them captive, but decide not to attack Earth-1 (note that they are not only trying to save Harrison Wells, but also change the future). If Grodd attacks, back to the start, with one dangerous gorilla removed from the problem.
Also, they may have hope that Grodd would be fair with them because of his past connection with Catherine (Season 2).
Why not attacking Earth-2?
The weak point of the above reasoning is that intuitively Solovar would attack Earth-2 instead of Earth-1, and putting Grodd as the leader would make Earth-1 the first target. That's probably true and I think it is not explained in the episode (I also found the scenario really meagre). On the other hand, they are heroes, so would not let Solovar put Earth-2 in danger, if it was its target. Another reason (pure speculation) that could explain the choice of the attack on Earth-1: it seems that on Earth-2, the existence of the intelligent gorillas is well-known, at least by Wells, so we may infer that gorillas and humans (army) may have reach a status quo on Earth-2 and are tolerating each other. Earth-1 is a new threat.