VLAN stands for Virtual Local Area Network, the word Local there is the answer to your question. Yes the VLANs will stay local at branch B, you don't need them at A. But you will need Layer 3 service ie. routing. What type of router do you have? If it's a Cisco 1700,2600,3600 with a Fast Ether int then you can implement ISL and trunk the VLANs to the ether port on the router and build Subint's on the router to route. You can then implement ACL's on each sub int to control traffic, create helper addresses for broadcast services etc.
Hope that helps.
:)