Even if you lie and say your eldest is 15 (which I am not a huge fan of, what happens if something happens and the flight is diverted to a third city (e.g. another passenger's medical emergency) that is an awful lot of pressure to put on a 13 year old. It would likely never happen, but it is the 1 in a million anomaly that counts), that wouldn't solve the problem since it says that the 11 year old would have to be "with someone 16 or older".

I am not sure many people are going to accept the 13 year old is 16.