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My contention would be that AtC could be played, with all heroes being set-aside while FW stays in play, remaining in the battle that will become a battle challenge. A new battle, separate from the one FW is in, begins and is a rescue attempt. Once that finishes, the heroes return and join FW in the original battle as a battle challenge.
Stays in battle. She's immune. If BtC is a cost benefit, there is no second battle, and nothing happens in practice. I don't think that's true though, so I think she'd stay around i nthe field of battle for the second one, and then be there for the side battle as well?
I'm still not sure I understand this ruling. Foreign Wives cannot be set aside, so she remains in the Field of Battle. The new RA takes place in that Field of Battle, because AtC does not create a new Battle Phase (like ANB, for instance). I don't understand why FW would not be part of the new RA.