I am a little confused on your setup. You said splitting the lines...so, is this one continuous line that is plugged in to the "relay" switch as well as destination and original? If so...no, you can't plug one line in to more than 2 devices.
You need to run the line from origin, to relay and then off a new port on the relay switch to the destination switch. If multiple are going from the same origin to the same destination then you either need spanning tree protocol running to prevent a loop, or all switches need LACP or trunking so you can group the ports together.
Also 90m is not the limit for cat5e, it is 100m of solid cable + 10m of stranded on either end. If you are running a link from switch to switch, you could conceivably get away with 120-130m between switches if using high quality solid core wiring, but that would be pushing it. Alternately you can use cat6/6a in between which is generally 1-2 AWG larger diameter as well as naturally lower noise, which should be able to let you stretch out the run an extra 20-40% longer in theory (most 5e is 24-25AWG and most 6/6a is 23-24AWG, plus better noise characteristics).
Just kind of up to the individual switches, wires and runs. I'd at least attempt a link using the length of cable it actually takes and see the quality of the connection before going to the complication of a relay switch.