We have been to Bali several times and have stayed in all Amans, FS Jimbaran, the Legian (club) and a few other, less famous places. Our son, who is now 14, has joined us on these trips. At his age, the most important is that the WIFI is great ;-) but he also enjoys trekking, swimming and other water related activities and joins us for sightseeing, and dinners. He really enjoyed Amankila (trekking, swimming, snorkelling plus cultural experiences), but actually preferred the Legian since the beach there had bigger waves for surfing and also there was more happening at that beach. In addition it is more likely that you meet other kids his age there if that is important. Seminyak is also more convenient for restaurants and shopping. However, I personally stronly prefer Amankila, so I would suggest to spilt the stay but you would need to add two days for this to be worthwhile. If this is not possible, ask Amankila to send you their activities list and see if he finds something there interesting to try to convince him that way. That is what I would do at least