The motors are 12v and are also running off of the 12v wall wort. The arduino sends signals to transistors that trip the relays through the digital out pins . I do use the +5v pin on the Arduino to supply voltage to actually trip the relays. I suppose this could be it...perhaps running the 5v to more than one relay coil could be too much. Maybe I should be supplying the 5v for the relay coils from the wall wort via a voltage regulator rather than straight from the Arduino board. I'll try this next.
I tried jumping a 330uf capacitor between the Vin and ground pins to filter out noise. No real luck there as the Arduino still trips.
Thanks for the help!
UPDATE*
Okay, using the +5v pin to trip the relays seems to be the problem. I used a 5v voltage regulator instead and it seems to have eliminated the reset problem. I guess I don't understand why I don't get reset issues when running off of USB power, because the board still has to supply the same 5v to the relays. Maybe with 12volts coming into the Arduino and 5v going out, its just too much power transfer for the board to take.