Thanks for the details, it helps to know some of the specifics. As @ScruffR has pointed out, I think we are still not all understanding what you want to do. For example, a 12V regulator is typically used to deliver a 12V output from a higher (buck) or lower (boost) voltage. If you already have 12V, then you don’t need a regulator at all but may need:
- Bypass capacitors to help prevent temporary voltage dips when a motor is switched on
- Diodes (like you have in your circuit) to dump reverse current when motors are switched off.
- Some current protection devices like fuses or resettable PTC fuses
Also, as @ScruffR pointed out, solder less breadboards are not intended to handle this amount of current. From what I can see on-line solder less breadboards are typically only used for 1-2A current circuits.
Have you considered buying a commercial relay board rated to handle your needs? Otherwise, you will need to use a soldered breadboard such as the Adafruit perma-proto and use solid core wire to to handle connections requiring more than 2 Amps.
Hope this helps,