There are two potential problems here, and you’ll need to do some homework to figure out which is the culprit.
The first possibility is that turning on the motors drops the DC voltage at the payload enough that the network circuitry has problems. The second possibility is that the motor controllers (ESCs) create electrical noise within the communications bandpass of the homeplug adapters (2 MHz - 30 MHz), which interferes with the operation of the homeplug adapter. You first need to perform a test to see which issue it is. You can do this by rigging up a test to run your ROV networking and CPUs off a battery pack, but sharing a common ground with the ESCs (which will still be powered over the tether). If dropouts still occur with the battery power, then it’s not an issue with voltage drops over the tether.
If the issue is RF interference with the homeplug signal, then you’re going to need to get some big ferrite beads that can handle the current of the ESCs, and place them on the power leads going to the ESCs. This will keep RF energy from making its way from the ESC back to the tether.
There’s a lot going on here that can’t be explained in a simple forum post. You may very well need to find an electrical engineer to advise your group, and round up an oscilloscope to take a detailed look at what’s happening on the tether.
Let us know how things work out.