Unfortunately, the baby probably disturbed most of the passengers in the immediate vicinity, including those in the back rows of J. I don't believe the airline is responsible for the temperment of an infant? Why would your peace and quiet be more important than that of the other passengers, including possibly, other status passengers. The flight attendant did her job by searching for a vacant Y seat for you. Good customer service sometimes involves not showing preferential treatment to one customer, in a situation which clearly disturbs many customers.

A good flight attendant would have noticed your predicament and would have finessed a solution. To blatantly move you to J, at your request, could possibly have opened pandoras box.