CatPilot - You have had the benefit of some very good and some very bad advice here.
I suggest that first you get a copy of the 777 roster and compare the actual, usable time at home, if you are on five days of lates or earlies SH there isn't a whole lot you can do with the few hours you are at home before and after work. It is unlikely that you will disappear "for weeks at a time" these days on LH, frequency of schedule means that lengthy hotel stops are kept to a minimum. Using Skype, for example, you can talk and see each other most days from most parts of the world.
My wife, also a very capable person, was glad to see the back of me for a few days at a time, then when I came home it was all 'holiday', LH worked for us. I don't think you can base your career on the preferences of just one person, there has to be compromise, other wise there will always be one satisfied person and one dissatisfied person in the house and that isn't good.