Too bad they don't have EDP. I did that too. You would obviously have better chances if you applied broadly, but I don't think it would look badly if, when asked, you said that you are only applying to this one school due to family reasons. As long as you show your commitment to medicine (i.e., "if not accepted this cycle, I will reapply, improve my application, and discuss with my husband the possibility of moving after I apply more broadly next year"), I don't see it being that big a problem. They understand that people with families may be more limited in their school choices, but you have to make sure it is not interpreted as a lack of commitment. Good luck!
Interviewers volunteer for the job and take time from their busy schedules to interview because they believe in the school and the community. It sounds funny from the interviewee end, but part of the interviewer's role is to sell the school to you. They've made a commitment to this community and will relate to your own commitment. Talk about your strong ties to the community, your commitment to being an active Washingtonian citizen, and your confidence in the fit of the school for you. You sound like a very competitive candidate; I don't think the number of schools you apply to will affect the outcome one way or the other for this one particular school.
I applied EDP to a school 5 minutes from where I live for a very similar reason - my DH owns his own business and it would be financial suicide for him to pick up and try to start over somewhere else.
Definitely meet with someone at UW and see what they say. And if you are asked how many schools you applied to in the interview, be honest. You are married, with a child, and if you don't have to separate your family you don't want to. I was asked why I applied early decision - I emphasized my family ties here but also made it clear that the school was more than just a location to me (ie - pointed out some aspects of the program that are appealing to me besides location).
Do consider residency also - if you need to relocate for residency will that be possible? I would speculate that residency is harder than medical school and would sooner attempt medical school without my spouse's help than I would residency.
Well, you do certainly sound like a competitive applicant. I'm always really impressed by high GPA's, though, since I haven't been able to manage that one since high school.
Rather than speculate more, why don't you see what the admissions director at UW says? In my experience, these are really nice people, who don't really function as "gatekeepers," but rather as PR folks, because it's in the school's interest for everyone to love them. Make sure they know how great you are, too.
By the way, 3 hours is a bit long. If it were 2.5 hours or less, you could move to halfway in between and everyone would have a doable, if unpleasant, commute. That was our plan if I didn't get in nearby. Terrible, unpleasant, but a plan.