The general recommendation is to install addition Ethernet cable in the house. Yes, you want wireless, but extending wireless beyond just two rooms may not work well. Two wireless units connected by Ethernet would be needed to give full wireless coverage. The main router does WAN and DHCP.
An alternative to Ethernet cable is Network over Power lines. This can be more costly that installing more Ethernet cable. The advantage is the existing house wiring is used. I have no info on this.
Also, routers can be set up as 'repeaters' or dependent AP devices that relay the signal from then main wireless router. Many routers do NOT have this feature and you hare to investigate before you buy.
Personalty, I have never been able to do the wireless only repeater. Yet others say it is easy. Here is a link that may provide more information about wireless repeaters for home use.
Universal Wireless Repeater - DD-WRT Wiki