Hook hadn’t counted on Emma turning on him, he thought he had the upper hand in that relationship, and if anyone was gonna do any double crossing, it was gonna be him. So I can see him not trusting her any more, (whilst at the same time being impressed by her), and going back to TeamCora instead, at least for now.
As for Cora giving Hook a second chance even though he failed to get the compass, it’s not like she’s got a lot of options right now. As far as we know, there aren’t many people left in FTL, much less people who have a passionate grudge against the same person she does. They both want Rumple dead, and if they work together, it increases their chances of getting the job done. Basically, Cora needs Hook.
I guess during whatever communication happens between Charming and Snow, the topic of Cora must come up. Is it any wonder Regina and Rumple wanna kill people who come through the portal if one of them is potentially Cora? Assuming that Cora is savvy enough to have considered the fact that she wouldn’t last long in SB if she pokes her head through the portal, that could potentially lead to the impostor theory coming true. Much easier to sneak into town as Snow, because even if Regina and Rumple set some sort of trap for those coming through the portal, Charming would see to it that Snow (and Emma) wouldn’t be caught in said trap.