Bragg's is a common brand of ACV with the "mother" in it. This is what you really want if you would like to have the full benefit. When you look at the bottle, it should be murkey, and have sediment. If you use this, you would want to shake it first, to suspend the particles of sediment.
Diatom probably is short for diatomaceous earth. It is a naturally occurring substance. I believe it is the fossilized remains of tiny sea creatures. There are several grades, and what you want is the food grade. It is often more difficult to find than the pool grade, but the pool grade has additives that would be harmful to birds. Food grade should say "food grade" or "food codex" on the bag. Try different feed stores for this (you may have to ask for it), rather than finding it on the shelf, and you should check around regarding prices, as there may be a wide variation. Once you have it, you can dust the entire coop and run with it, if you like. It is a good idea to use a mask when working with it, as it is very fine, like flour, and can be inhaled by you---which can be hazardous.