Bird in the hand is important, but it sounds like a difficult and risky move.
Can you find some other offer in FL before you have to decide on the AK offer? Will the AK folks commit to a 2 year contract to allay your wife's concerns? If not, will they commit to helping you find something else nearby in AK? If not, will they commit to some severance payment if the job doesn't last 2 years?
If you can't find anything better by the time you have to decide, then it looks like you'll have to take the AK job.
Kids are pretty maleable with good family support. Don't worry about your little ones too much. I moved a lot through grade school (GA, OH, GA, OH, OH, OH, ...) and turned out OK (except for this nervous twitching eye... ;-)
I know this doesn't help much. Good luck with the negotiations and the search!
Cheers,
Scott.