Setup central DHCP/mutliple sites-scopes

I have three sites. Each needs thier own ip addresses because I will have routers inbetween them. DHCP, local DNS, Wins and the Internet connection are all at Site 1.
Site 1 router is 38.123.123.1
Internet router is 38.123.123.2
Site 2 router is 38.123.124.1
Site 3 router is 38.123.125.1
When I configure the DHCP scopes do I need to put both the Site router and the Internet router for Site 2 and 3?
When I configure the DHCP scopte for Site 1 do I include all four?