@Delphic: I disagree the moment Logan saw Hope the first and only thing he went in for was the kill. And with that in my mind couldn't Cyke and Cap just team together where Hope is locked up somewhere that Cyke and the gang can train her whilst the Avengers try to stop the Phoenix Force.
Cyclops doesn't want Cap's help. "It's a mutant problem." is what cyclops said. Cyclops doesn't want hop locked up. He doesn't want to stop the Phoenix. He want's to control it. Cyclops would never team up with Captain America because Cap's plan directly interfere with his own.
Maybe you're right about Logan though, but it seems out of character for him to kill a kid. Especially after opening the Jean Grey Institute for Higher Learning. He's probably scared to death that the Phoenix will return and kill everyone he knows again. No one has thought about what Hope wants though. She obviously doesn't want to go with Cyclops, and he's forcing her into this against her will and keeping her captive on Utopia technically. The Avengers want to lock her away because they think she is a threat, and Logan has threatened as you say to kill her. If I was her I would run for my life too and get the hell away from everyone. If I'm really with anybody on this, I'm with Hope, and I hope eventually someone can come to her understanding her predicament instead of using her for their own selfish desires. Unfortunately that someone will probably be the Phoenix itself.
He does say Hope is a mutant problem but only because Cap showed up unattended to Utopia making demands which showed Cyke that Cap does not trust them. If Cap would have called ahead of time called Scott then explained to him calmly that the Phoenix Force is destroying worlds and Earth is at risk I'm sure Cap can get that point across in a way that Cyke would agree because if they did that at that time they'd still trust each other to an extent. Scott got all mad because Cap showed up with his Avengers to take Hope. I mean as I've said Scott wants to train Hope to control the PF Cap wants to lock her away why not have the Avengers put her somewhere they can monitor her (locking her away) with the Xmen who will train her to control the PF (train Hope) in case the Secret Avengers fail in their attempts to defend, both parties then could have their requirements met.
Yes it's out of character for Logan to kill a kid but it just seems him going for Hope isn't really about the PF but I think he has an agenda deep down. He wants to prove to Scott that there is no Messiah iirc he doesn't believe in the whole Messiah business. I mean why didn't he do the same thing to Quire or Rachel both in one way or another connected to the PF itself, why didn't he tell the Avengers to lock those two out and just lock Hope up.
I sort of just realized that were technically having the same conversation on two different threads, so I think I'll localize my replies to this main topic of this tread which is "What do the Avengers plan to do?" and like I said earlier they only want to lock her up and keep people safe from the possible threat of the Phoenix. They wanted to cooperate with the X-men, but things just didn't work out it seems.