We've rented from National the last few times. They have locations at the airport, Road Town, near Nanny Cay and at West End, so they are very convenient for drop off and pick up from almost anywhere you might be. They'll pick you up and drop you off too. We were able to just leave the car with TMM last trip, so didn't even need to take the car back to them. Had a party of six adults in a Honda Passport two trips ago, I think it was about $90/day and it worked out fine. You should be able to do just fine with three adults and three kids. They also have minvans, vans and suburbans, although I would probably stick with the Passport or Tahoe with the third row seat as the longer wheel bases can be a bit tricky on the switchbacks.

Once you decide to rent a car, there are tons of options on where to stay. Another one to consider is Heritage Inn at Bananakeet. They have two bedroom suites (with lots of beds, you could probably get your party of six into one of these suites and still have a private room for you and the husband), pool, restaurant and bar on site and incredible views. We spent a few nights there last trip and absolutely LOVED it. The staff there couldn't have been nicer and more helpful either. In fact, our flight was quite late so we didn't get there until about 9 or 10pm. They stayed open just to serve us dinner and drinks, totally turning around a long and somewhat harrowing travel day. Just can't say enough good things, highly recommend.