The setup would be as the diagram below.
The issue is that when in Room A, the WiFi signal from the router/modem in Room B is flaky, causing the devices in Room A to drop the connection all the time.
I can easily add another 3-port Powerline networking plug in Room A (I have them elsewhere) to get wired connections into the Wii/XBox/Sky TV box.
My question: I want to get the two WiFi devices in Room A connected via the 'mystery box', which will allow a strong signal since it is in the room, and which will use the (effectively, via Powerline) wired LAN connection to the modem/router in Room B, and not just pick up the existing WiFi signal from Room B,
So do I need something in repeater or access point mode for my mystery box, and can it be made to work over a wired connection?