You can configure the RPi as a bridge, including between 2 USB wifi interfaces, wired interfaces or any combination. Be aware, though, that most of the USB "nano" type wifi adapters don't perform at what you might expect from the packaging. I tested Edimax, TP-Link and generic adapters on a desktop PC, and none would connect at any higher than 54 Mbps in the same room as my wifi router, including the "n" compatible versions. The generic was limited to 35 or so Mbps.
The RPi 2B itself can bridge traffic at over 100 Mbps without a problem, despite the limitations of the USB-Ethernet controller. The cheap wifi adapters are the limitation. Using 2 wifi adapters, I couldn't get more than 10 Mbps of throughput. If this is sufficient, or if you're willing to buy adapters that cost more than the RPi itself, along with the appropriate antennas, you might be able to do this satisfactorily.
I am not sure if the device shown in the window on your drawing is just an external antenna, or a wireless-wired bridge. In any case, I'd expect to have to use some external antennas to get it to work unless that outdoor antenna is located very near to your house. So while you might be able to get a RPi to work, there may be special-purpose devices out there that will cost less in the end to get working.