Protecting microcontroller from drastic changes in load on power source
That all depends on your circuitry.

However, as a general rule you would NOT put your load on the same circuit as the logic of your controller. Driving 18A through your power and ground traces shared by the controller can induce significant problems for the micro including shutting it down or resetting it.

The logic section should have it's own connection from the battery through whatever regulator you are using. If you are not using a regulator, then at least a small in-line inductor and decent bulk capacitance should feed the logic.

The LEDS should NOT be powered from the regulator, they should be direct from the battery and driven with simple constant current drivers if need be. 

Similarly, the return ground should be separate and connected together as close to the battery as possible, if not at the battery itself.

BTW: The only way you could get a PUSH effect is if there is a sizeable amount of inductance in the power path from the battery to your power line. Since you have not indicated what you are using for power conditioning, it is impossible to comment if that will indeed be a factor here.