A splitter would not work. You'd use a hub or a switch with at least 3 ports.
Connect from the outlet powerline adapter in your bedroom to any of the ports in your hub/switch. Then plug your bedroom computer and PS4 into any 2 other ports on the hub/switch.
The old router should work, if it has a built in switch (w/3 or more switch ports). You would want to disable the routing functions on the router though via its admin menu, so you are only using it as a switch. Then you would connect from the powerline to one of the switch ports on the router; not to the WAN port.
One other note: if the ports on the hub/switch (or old router) don't support Auto MDIX, you would need to use a crossover ethernet cable to connect from the powerline to hub/switch.