The reason I used a 5 volt relay is because that's what I had available. I recently bought a 12 relay to try. Thanks for the transistor mosfet suggestion. I haven't had time to try it yet.

I did monitor the power supply while the circuit was operating. I used a fluke meter that could catch peak voltages. During the horn on cycle the power doesn't drop off more that a few hundred millivolts.

I don't have decoupling caps at the chip but I'll try that also.

Thanks for all the ideas.