Unsympathetic attorney here. A couple thoughts:

(1) Your fiancé is probably right that with only a month or so of actual legal work experience going into your 3L year, you're not making the looming job hunt any easier. And I can't help but agree with your wife that you need to figure out how to do both. As an attorney in the real world, you're going to have to figure out a way to manage your time better. 15 hours a week at a job is really nothing, and even if you're actually working more than that, I find it hard to believe that you can't find time to get all of your schoolwork done with the rest of your day(s).

(2) Stick it out at the internship. Maybe you quit, but then you're left with the uncomfortable situation of having to choose between leaving the internship off your resume (in which case, you've been doing this law school thing and only managed to get a month of experience), or putting it on there and trying to explain why you only got a few weeks of experience there as well. Don't put yourself in a position where it's going to look like you can't hack it as an attorney, because by now you should realize that being an attorney is a demanding job. As an employer, I wouldn't want to hire someone that doesn't have any real experience and/or someone that quit partway through an internship for any reason other than that there was a death in the family. To me, that screams "not motivated," "not mentally-tough," and "weak-willed." Frankly, you should take whatever experience you can get, whether you're interested in it or not, because some of it is going to be useful to you at some point, almost regardless of what field you're in. And in this case, I would be of the opinion that you need to stick this one out if only because you committed to doing so at the start of the semester and you've given your word.

At the end of the day, an attorney's most important asset is his reputation, and you need to think about what yours is before making your decisions, because that reputation starts now.