Excellent advice from FDW - you really won't have a relaxing holiday if you're constantly keeping your kids quiet. Worse still some will come on here and complain how noisy and unruly they were.

Wait to stay at the Amans when you and your wife are having romantic break away just the two of you. With 6 nights I would be tempted to just stay at the FS Jimbaran and take a trip organized by the hotel to Ubud/ rice fields etc maybe taking in their hotel at Sayan to see whether you would want to stay there next time. Or if you stay at the FS Sayan you could organize a trip to their hotel at Jimbaran but having said that my kids were always happiest on the beach but they do remember their trip to the monkey forest from when they were about your eldest kids ages - don't take the baby in possibly!