I would think that 3 resorts in 6 days is a bit much. Between the packing and unpacking it doesn't seem that it would be that relaxing of a trip. Honestly with only my two kids, I probably wouldnt move at all over a six day period. But, I would wager that Nusa Dua isn't the greatest place to spend 6 days so I can understand the desire to move.

Now, I'm going to strongly discourage the Amans. At least Amandari and Amankila. I've never been to Amanusa so it's not really my place to say. But, if you're 6/8 yr old boys are very social and love being around other kids, than Amandari and Amankila probably aren't the best option. At least when we were there we didn't see any other kids at all. I would wager that the Aman staff would do a great job with kids, because they do a great job with everything but at the same time I know both Four Seasons have kids clubs, which would most likely attract more families. MY 6 yr old would probably find more to do at the FS. Sayan also appears to have a family suite option, which looks to be a great option. I'm thinking that at the Amanusa you would need at least a two bedroom villa and at Amandari I think that the Amandari suite has a two bedroom option. Finally, if memory serves me correctly, is cost. I'm all for investing in experiences, and I look at our Indonesian Aman experience as well worth the cost but it is significantly more than the FS. I recall for our trip it was about 2x the price. The FS frequently run 3/4th night free deals, which are useful. For a family of 5, that chunk of money can make a big difference. Though, I do recall seeing that the Amans had a free night promo through FHR (which I had never seen before)...

So in summary I think that:
The FS will likely have more kids around. Also dedicated kids club facilities for doing stuff.
More amenable room types for families of 5 at the FS
Significantly cheaper...

FDW