Well I am not there but a few things not picking an 11 year old is not a 15 year old, there is alot of maturity difference, esp since a 15 year old is either dating or ready to date.
But at the end of a day a 11 year old is still a child and alot of things are going to happen in thier life they are not going to like and at times they are just going to have to be forced to accept things.
I really don't feel letting them run away from the issue by living somewhere else is the answer,
For several reasons,
You never said where his father is ( and does he and 15 year old have same fathers)
it is very possible the 11 year old has grown up feeling he is really the man of the house and this is a real threat to his position
MY opinion you start him in family couseling which would be forcing him home after a while