You are simply overloading the on-board regulator of the Nano I think. Under USB power its
not used, but from 9V on Vin it will be dropping 4V and carrying all the current for your relays and
displays.
Use a 5V regulator or DC-DC converter to power the displays local and remote and I think
it will be OK
I do have some questions about the circuit though:
Do your relays have built-in diodes? I hope they are very low current reed-relays with
in-built diodes, as those are the only relays it is safe to power direct from an Arduino pin.
Do you realise that sending a high speed logic signal 11m through a cable is generally a bad
idea and will lead to various issues? What speed are you clocking the displays? I'd suggest
keeping that speed low, and adding 100 ohm resistors in series with the clock and data lines
at each end of the cable to help tame signal reflections