I still dont understand how you wanna use spliters
Preferably the router is installed as close to the outdoor antenna as possible to minimise cable loss. You put a 2 way splitter right at the antenna port of the router. One output runs to the outside antenna and the other output runs to an indoor antenna.
At my friend's place the outdoor antenna is mounted on the side of house closest to the AP down the road, so his outdoor Yagi is pointing away from his house. The backlobe of the Yagi is not sufficient to give coverage inside his house. So the signal is split, 90% to the outdoor antenna, and 10% to an indoor patch pointing into his house. The patch has 9 dB gain, compensating to a large extent for the fact that only 10% of the power goes into it.
At my place, my outdoor antenna is mounted so that it points basically slightly over my house into the general direction of the AP down the road. By tilting my antenna slightly downwards, I get good coverage inside my house without sacrificing too much on connecting with the distant AP. So I don't need a splitter or a 2nd router as was suggested earlier in the thread.
My router is set to transmit only 25% power, yet through my asbestos roof in the computer room I still manage to get -62dBm from the outdoor antenna. During heavy rain, I maybe lose 3 dB, due to the roof acting as a shield.
I might add that I haven't checked for any commercially available splitters online, and I am not sure if you will find a 10dB splitter. You may find a 3dB one, meaning a 50/50 split. And all splitters have loss, but its specification should mention this.
@Robone, I would get on the roof with a laptop and router, and using its own antenna see if I can connect to the other dude also on his roof with his router and laptop. Then if you can get a signal strength indication from the router, it is easy to calculate the signal you would end up with using your panels and maybe a splitter.
just remember that a radio can only act as AP or client, not both at the same time.

My Linksys WRT54GL router is on AP+WDS mode, so I can connect to it from my pc's USB-WLAN and the router connects to the AP across the road which is connected to the internet.