Resistor-only solution to split 19V 3A to 3.3/5V and 12V 2A with common ground?
This is a bad idea! In order to use a resistor divider, you need to have a good feel for how much current your devices use. Also, while you may have a lot of resistors, you will need high power resistors. Resistor-divider power supplies are EXTREMELY inefficient

For powering the microcontroller, we need to make sure that the voltage doesn't exceed the maximum rating, or else it will die. For ATMega parts that tolerate 5V, the maximum input voltage is 5.5V (5V +10%). Lets suppose that the current through R1 and R2 is 10mA. R1 will drop (Vin-Vreg) volts, and then using Ohm's law we can find the resistance of R1: (21V - 5.5V)/(10mA) = 1.55 kOhm . R2 will drop the voltage Vreg, so once again Ohm's law shows us (5.5V)/(10mA) = 550 Ohm .

How much current can this supply source before we start having funky issues? This is hard to tell for me because the AVR has such a range of operational voltages (5.5V to 2.7V). If we say that we shouldn't fall below 4.0V, then the maximum load current is equal to: (Vin - Vreg_min)/(R1) - (Vreg_min/R2) or (21V - 4V)/(1.55kOhm) - (4V/550Ohm) = 3.7 mA . R1 will dissipate the most power, and if you're using 1/4W resistors, you need to be careful here. The power dissipation of R1 will be most when the load is drawing the maximum current: P = (Itot)^2*R1 =10.97mA^2 * 1.55kOhm = 187mW . Increasing Iquiescent (decreasing R1 and R2) will increase your maximum current, at a major cost to power. Increasing the operating range will decrease the power, but may cause issues.

If you can identify the current for each leg that you are switching, you may be able to just add a series resistor with the light bar. For example, if one of the legs normally draws 100mA at 12V, then you could add a series resistor (Vin - 12V) / (Iload) = 90 Ohms
and things should just work out without providing a constant 12V.

Note: Use as low of a voltage on your power supply as possible. I'm not sure if this is adjustable, but if it is, use 17V instead of 21V.