The possibility of Alfredsson signing somewhere else is real.
I don't see why he'd have to uproot his family either. September to April / May is not that long. Either way the guys are on the road half the year anyway.
Kids will be in school. Wife will do whatever it is she does.
Have you heard him interviewed about retirement? Spending time with his family was a big check mark in the retirement column of that decision table. I really doubt he'd sign somewhere else.