Problems with brake discs
It sounds like your brake pads are contaminated with detergent or petroleum (oil) products. If so, you need to replace them.  

This is a common problem, which can be solved by washing the brake rotors with IPA, and replacing your brake pads.  It sometimes happens that a pad will get contaminated by chain lube or other common bike lubricants during the washing process of a bike service, and should be no big deal to fix.

As this is something that any shop worth 2 cents should know, they are either incompetent, or dishonest with you.