I doubt if you're right. He has one modem (unsure where it's located) and wants WiFi in the living room and WiFi in the bedroom also. As I read is, there is only one modem.
And he wants to use the existing Ethernet-ports in both rooms to provide WiFi, so his laptop and phone work in both rooms. Seems a reasonable wish.
Usually, in an appartment (unless it's a really big one) WiFi in one room can work well in the other room. So that's the first thing to try.
If it doesn't work satisfactory, a repeater, a mesh network or a power line extender are common solutions. But if there already is Ethernet in the second room, another independent router should work also in my opinion. But it would form a separate network, with it's own SSID and password.