Some 30 Unison activists, campaigners and parents protested at a youth event attended by Labour mayor Ian Stewart on Tuesday of last week.
They are fighting to keep the Grange Children’s Centre open as respite care for children with autism and learning disabilities.
It is under threat as Stewart and the Labour controlled council implement Tory cuts.
Stewart described parents as a “rent-a-crowd”.
The protest forced him to answer questions about Labour’s plans to make children aged over 14 use an adult centre, cutting respite in half for both adults and young people.
Stewart has now agreed to meet with campaigners.