I just went through a (somewhat) similar situation.
I’m an engineer who’s been working for a consulting firm for the last few years. I felt like I was stagnating in my position, so I passed out two resumes to other consulting firms. At around the same time, I sent in an application to a public water/sewer utility in response to an ad. Being a widely advertised position, I felt that this job was more of a long shot. Finally, I passed a resume to a friend working at a power plant.
Both consulting firms promptly called me in for two rounds of interviews, and both made me offers. I requested that the firm that made the first offer extend their offer to finish the interview process at the second. They did so, and I ended up accepting the first offer. While I hadn’t heard back from the public utility or the power plant, I felt that I had stretched the consulting offer extension as far as I could, and besides, I felt that both of the other jobs were long shots.
I gave my notice, and started at the consulting firm. My first week at the new job, I got the call from the public utility, over six weeks after I applied.
This put me in a bind. The public utility job had a lot of benefits compared to any consulting firm, the biggest being no travel. So I went in for the interview. During the interview, I told them that I had already accepted and started a job at another firm, because they had taken so long to respond. (Besides, they would find out anyway when they checked my references.)
The interview went well, but they still moved very slowly. Six weeks after the interview, I had a job offer in hand, and decided to accept it.
With great trepidation, I gave my notice at the firm I’d been working at for six weeks. I was honest with them, and explained the situation. Fortunately, while they were disappointed, they handled my resignation very graciously. I worked my last two weeks there (and worked as hard as I could, so as not to leave a bad impression).
I must have done something right, because they told me that if the public utility job didn’t work out, to just give them a call. My (former) boss told me that I certainly hadn’t burned any bridges.
Now for the twist. Right before I started at the public utility, I got the call from the power plant, over two months after passing on my resume. At this point, I had no intention of going through that again. I regretfully declined the interview, telling them that I had already accepted another job offer. I also called my friend, thanked him, and explained the situation.
So anyway, you have to do what’s best for you, your family, and your career, but you also don’t want to burn bridges. In the OP’s situation, if one or both of the other jobs are clearly head and shoulders above the one you accepted, then go for the interview(s). To get them moving, you might mention that you have a job offer on the table, but I definitely would not tell them that you had already accepted it. If you decide to accept one of the other offers instead, be as apologetic as possible when you tell the first company.