This is a short story dating back to the 1980s or earlier - I read it in my school library in the late 80s/very early 90s. It's about a world in which underdeveloped planets were forced to hand over children for adoption to wealthy offworlders. They are told to have a 'birthday party' for two year olds who are then taken away. The first scene is, indeed, a family trying to have a 'par-ty' for a small child who is then taken.
Many years later, few of the adopted children know they were adopted. One of the children - perhaps the child taken in the first scene? - meets an old friend of his in a bar who is talking about composing a song about searching for home. The song becomes very popular and suddenly these people start feeling a need to find somewhere they barely remember. The story ends with news that a planet which had been thought of as nearly empty was erupting into rebellion as these missing children return.
It was one of a collection of short stories in an anthology that I found in my school library in the UK in the late 80s/early 90s. I think the cover had an image that looked like a tree lit up in the dark but I'm not sure.