Are you a parent? If so, please share your secrets in quieting a fussy 2-year old, as it sounds like you’ve never had this problem.
Spare the rod, spoil the child is no secret. It’s not your job to be your child’s friend.
On our long flights overseas, I see a lot of parents of very young children. Most are really good kids. Nothing can really be done, however, about a sick infant beyond the mother's comforting the child and your patience with the noise. Otherwise, I suspect that a good kid on the airplane is good at home. The pain in the rear on the plane has learned that such behavior gets action and wanted attention.