Connecting two wireless routers to one cable modem

I live in a trailer just a few yards from my bother's main house. The cable modem is in my trailer and an E1200 linksys wireless router in his house - connected by an ethernet cable. The router is refurbished and apparently not strong enough to support the level of wi-fi being drawn off it. I bought a new E3200 linksys router which I plan to put in the trailer. What I need to know is if I can use an ethernet splitter connector adapter to run one ethernet cable into the house to the E1200 and another ethernet cable to the E3200 in the trailer. Will this even work? And if so, will it weaken the wifi signals from the routers? I think the E3200 will be enough for the trailer and the house - considering the E1200 - when it was in the trailer - supplied 3 bars to the far side of the house. But my brother may insist on keeping his own router, so that's why I'm asking.