OK, what you need is a means to convert that 20V battery down to 12V and do it efficiently. The device that does that is called a buck converter, and you can get one here:
https://www.mpja.com/5A-Buck-Converter- ... /34736+PS/, which conveniently has V and A meters and a knob to set the voltage. No soldering required; doesn't get much better. Efficiency will be around 90% or better.
When you say appliances, what exactly do you mean? LED lighting will do fine, but that 12V trucker's coffee pot will drain your battery in a minute. Your Dewalt battery can probably deliver about 2A for 15 minutes, then it will be done until you can recharge. Remember, these things are designed for intermittent use at high loads, like a drill, or constant use under low loads, like a flashlight. If you are trying to save money, you would be better off springing for a 35Ah AGM battery and a 3A charger which you can get for around $80.
PM me if you have specific questions. I'm an electrical engineer and can probably steer you in the right direction once I understand what your needs are.
In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.
-- Antoine de Saint-Exupery