Not a good idea. Use direct port writes to set the pin states at the same time.
It would be much safer to use a transistor to switch the relay coils, and to use a separate power supply for them. Or, just buy a relay board designed for Arduino.
The Arduino on board voltage regulator is NOT designed to handle significant loads and may overheat in your scheme. Avoid using a 12V supply on Vin, as that makes the problem worse. 7V is much better.