Not entirely sure what you mean by "handbreak" wire, I assume it's for the switch that detects the handbrake state and mutes the video when your handbrake is not on? Just in case you weren't aware, bypassing this feature and displaying full motion video on the display is technically illegal (at least here in VIC), you can be booked for it.
I gather you're trying to use the relay to pull the handbrake wire to ground to emulate the handbrake switch being "activated"? I don't have any experience with this style of headunit, but from a general electrics standpoint, why do you need a relay? I'd just tie it to ground.
But to answer your question, the remote line will *probably* drive a relay and provide enough signal to power the amp up, if not there are some other options.