Hi Eric and welcome to the Forum. Polishing and sanding is subject too vast to go into in detail here but I can give you some insight into it.
Firstly polishing and sanding requires lower speeds than most conventional tools as not to overheat or burn the tools or workpiece. They generally require more torque as there is more resistance in the process. The main difference between a sander and a polisher is just what they are used for but polishers will generally have the ability to go to a lower speed than a sander. A rotary polisher just rotates and is most often used for polishing and sanding plastics, paint, stone, marble, glass and metal. Most woodworkers use an orbital sander for finishing which oscillates and is less likely to leave sanding lines in the wood. The next thing to consider is the abrasive used. Aluminium oxide is the most popular for wood but is useless on hard or dense materials like glass, marble where silicone carbide and other mineral powders are generally preferred but they are more expensive and often considered too harsh for wood' although I have no problems using them myself on wood using just a rotary sander. Zirconia Alumina is a popular choice for metal.
As for polishers, most polishers used for polishing cars, being realistic, are too large and clumsy for detailed work on wooden furniture but could be used on the flats with care. Smaller ones used for stone and metal are expensive. If your headlight is glass it will be tough task to re-polish. If it's plastic that will be much easier and you could use paint or metal polish with a sponge pad or felt. Speed would be as slow as possible for polishing around 500-1500 rpm. For sanding wood, depending on grade of abrasive and hardness of wood about 1200-3000 rpm. As you mention using a drill, it is usually around the correct speed range but they are more difficult to control. Also most sanding and polishing attachments have a 14mm female thread. You can buy an adaptor to go in your drill chuck or just use a cut off 14mm bolt.
I don't know anything about UV protection coats sorry. I could go into endless detail but this should give you enough of a guide to enable you to play around to get things right.
Not quite sure you've phrased your question 100% clearly. You can polish your headlamps with sanding/polishing tools if the headlamps are plastic. If you sand a plastic headlamp lens you will go through the UV protection coat. You can re-apply some kind of UV protection coat after you have sanded and polished the headlamp lenses to your satisfaction.
There are kits out there for reconditioning headlamp lenses (3M make one I think) that give you varying grades of wet-and-dry sanding heads on spindles that fit into a normal power drill (you need one with speed control mind you). They will also contain a soft polishing head too. I believe you can buy a dedicated polishing power tool, but that's a matter for whether you want to spend the money.It won't do the required sanding for you though...
As for your wife, I would imagine what she really needs to sand furniture is a detail sander (to get into the nooks and crannies) and plus some hand sanding blocks, both the rubber and foam types - not stuff that is meant to polish car headlamps.
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