Ok, amp one stays on, amp two cuts out. If the radio stays on then I think you can rule out the radio install. Unless you have some sort of RCA problem (spike in the input)
Are the amps connected to the same power and ground (did you use distribution blocks) If not I would recommend having common connections (makes diag. much easier)
Now if there is no rca problem (swap rca outputs to the amps to verify) that leaves remote lead - which if your other amp is drawing to much current from the turn on lead and you simply spliced the two amps leads together, this could also be a problem (not likely, but possible)
Best thing to do, go buy a voltmeter (digital) from Wal-Mart or wherever. Best $20 you'll ever spend and it will answer all your questions better than we could all guess.