Well, the very first thing I'd say is don't ever think of family as an intrusion in your time. If you haven't done so lately, fall down on your knees and give thanks that you have them!
Business, now that's another thing Since taking on a managerial role, I've had all manner of bizarre things to deal with. Yesterday I lost an employee to lung cancer and a student had an emergency appendectomy, and that capped off a week in which I had to deal with some $1M+ financial and personnel issues of the usual make-or-break variety. That's a bit atypical but... yeah, the day job(s) can be a lot to handle. All of my predecessors had major health issues after a year or so. For whatever reason I am doing fine, probably because I proceed with the faith that I was chosen to manage this stuff because I am the sort of person who can do it without wigging out. Which means that it's just a matter of calling timeout and finding my strategy... and putting one foot in front of the other.
So for me, photography is a form of mental oasis- a place to go when I want to set things aside and clear my head... while kind of chipping away at those other things subliminally, in the background. And I suspect that the reason why I can deal with the above-mentioned issues is that I have that place to go and collect my thoughts. For me, it is very beneficial just to dip into APUG a few times a day during a break, engage in some banter, think about something other than whatever stress just arrived in my inbox... and just let the earth rotate without me for a few minutes. And when I have time, the most relaxing thing I can imagine is to set up a still life or whatever, or just jump in the car and chase some warm light through the hills, with a bunch of loaded cameras in the back seat. Quite therapeutic.
I suppose that what all successful multi-taskers have in common is their own mental oasis, whether in the form of photography, writing, music, sport etc. I've known quite a few people who did lose sanity over relatively minor things, and all I can say is when the stakes are really high, you need a very clear head. You cannot get bogged down in the situation. What's so great about photography is that it's all about finding the right perspective. Photography really trains you to keep "the big picture" in mind.