I'm going to totally overgeneralize here. If you want to work in the US, the best international schools are comparable to the elite schools in the US. If you want to work internationally, then the top international schools are more like the schools in the ultra-elite cluster. But generally speaking, Harvard is in a class of its own, both domestically and internationally.
A part-time law degree will not help you get into any of the top business schools. In fact, my sense is that the top schools would view it negatively, as diluting their brand by bringing in someone with a lesser grad degree. By lesser, I mean both part-time and lower ranked school. There's a real stigma in the legal community about part-time law degrees (at least at the big firms I'm familiar with).
A JD from a top school
may help with admissions. It will depend on the school. Some schools seemed to value it a lot, while others seemed to treat it as a non-factor (I have a JD from Michigan). In all cases, the 5 years of my life (3 getting the JD, 2 practicing law) could have been much better spent on other things if business school is the ultimate goal. So my advice to you is if your ultimate goal is to get into a top business school, focus your efforts on other stuff rather than getting a JD or PhD. A top grad degree may or may not help, but it's certainly not worth the time and expense if the key benefit you seek is a little something for your business school application.
I can't yet say whether a JD will will in the business school job search. I've interacted with a lot of business school people this past year and my sense is that in certain professions, the JD will help. I believe that some banks and consulting firms may give credit for the JD (school reputation matters a lot here) and possibly for some of the time spent practicing law. I practiced in capital markets at top law firms, so that translates directly to many investment banking functions; and most top consulting firms are well acquainted with hiring burned out JDs. If I'm lucky, I hope to get credit for a year or two of associate service. I think that potentially, some specialty employers, like certain private equity companies or hedge funds, might value the legal experience and expertise. So, a JD could help you in your job search, but 3 years working at a top consulting firm or bank would probably be more beneficial; again these are better options if your goal is to get into a top business school and pursue a career from there.