I remember "Dragon's Teeth" differently. She allied with them for a very KNOWN reason--she needed help to get off of the planet and escape from the Turei and the Vaduaar claimed to be able to help Voyager use the subspace tunnels to get a shortcut home. That said, she remained wary of them, especially after her crew found their true history. When she found out how untrustworthy they had been, she said, "We said we'd try to help you make a new start, and I want to keep that promise, but I can't ignore history, Mister Gedrin." She would have been a fool to pass up the chance to have allies in defeating the Turei and in finding a shortcut home, but she was smart enough to keep her eyes and ears open about the Vaduaar and anticipate their treachery. I think she did well in that situation.
The Borg alliance is open to question, I suppose. She knew it was a "pact with the devil," but sometimes it's necessary to roll the dice when your back is against the wall. She made what she thought was a good decision based on the facts "as she knew them." Right or wrong, her daring decision got Voyager through Borg space and even garnered a former drone who gave them a leg up in dealing with the Borg at later dates. It's open to speculation how she would have handled the Borg differently if she hadn't been injured.
In "Alliance," the attempted armistice with Seska and Kulla was undertaken at Chakotay and Tuvok's suggestion--and only after they worked at convincing her. It failed, but I suppose it was something that had to be tried at some point. Yet, she wasn't "incredibly trusting" then, either, unless you mean she was trusting of her advisors that the attempt was worth trying.
Janeway consistently did what she thought was right, but usually had an alternative plan in her back pocket, just in case--"Counterpoint" is a great example of that. The only time she was really "caught up" was in "Bliss," when the entire crew was similarly fooled--except for Seven and Naomi, of course.
