Best way to power an Arduino with externals modules?
If you are powering your modules over a fairly long wire, when the relay actuates there will be an additional voltage drop across the power feed wires. Therefore I suggest you generate the required 5V locally at each module derived from a raw 9V supply derived from the Arduino. A search of Ebay, Banggood or possibly Alibaba should turn up some suitable cheap PSU modules. For example on Bangood there are these.
I assume you have sufficient decoupling at each module that any transient will not affect the sensitive circuits or feed back to the Arduino.