Can you charge Bosch 18V batteries from your car

You have the basic concept down. Your challenge will be sizing.

• What's the minimum possible load you can put on the system? For instance, don't use an inverter to run lighting. Run the lighting direct off 12V, and there's a huge variety of 12 volt LED lighting: from screw-in bulbs, spot or flood lights, LED strips that let you freestyle your lighting, etc. No problem getting iPad chargers for 12v, every gas station has them. A surprising number of internet routers and TVs will also run on 12V directly (partly, this is for campers).
• Inverters are not efficient. Put every load you possibly can on 12 volts direct. Simply at idle, with no load at all, it consumes 12-15 watts, or all the power your solar panel makes on an average sunny day. Obviously you only want to run it only when absolutely necessary for loads you can't get in 12v versions.
• It is usually cheaper to make loads efficient than to make your system bigger to handle inefficiency.
• If it's forgotten and left on, put it on a timing mechanism.
• Once you have your loads down to practical minimums, you can think about sizing the battery and solar panel for your loads.
• Make your battery's amp-hours 3-4 times bigger than your expected load. If you "bottom" a lead-acid battery regularly, you will greatly shorten its life. It's unfair but true.
• Size your battery for your "burst" usage, i.e. so it can make it through your hardest day's usage, and so typical days' usage use less than 30% of its capacity.
• "Battery protectors" are readily available, the best are probably those which disconnect your car's battery while it still has enough juice to start your car. The solar panel (charger) should go straight to the battery (fused of course).
• Size your solar panel to fully recharge your battery in between uses.
• How many days can the system function with no usable sun? (how often will this happen?)
• How quickly will it recover from a deeply run down battery?
• Fuse everything, to protect your wires and battery from catching fire or taking damage.

It really all depends on your situation. I have an application with a fairly large battery (about 300 pounds, NiFe) that burns a 60 watt spotlight for 3-6 hours a weekend, then has all week to recharge. A 20 watt panel is plenty, even when laid horizontal and covered with plexiglas and dirt.

This isn't one of those games where the goal is to use only this bag of parts, right?

Charge the battery with the solar panel

Simply connecting a solar panel to a battery will not do what you want. It will overcharge and wreck the battery. You need a charge controller between panel and battery. This is a keystone product that will make or break your build.

Good ones are hard to find. Generally the ones sold at chain/big-box retail stores are foreign dreck, often with reputable brand names slapped on them. I prefer using a low-end controller from a well-reputed company in the solar business like Morningstar. Unfortunately many of these are specialty products, so you just have to read up on solar-power forums and places like that to see who's regarded as the best.

From there, it's a simple affair to connect solar panel to charge controller, and charge controller to battery.

A good charge controller will not need you to throw switches or change wires.

Hook up your loads

Since your goal is lighting, get 12V lights. The point is to use 12V lighting throughout, run straight off the battery. Don't even think of running an inverter to run 120V lighting, that's just crazy.

Off-grid power is too precious to use anything but LEDs for lighting. Nothing else is efficient enough. You don't want to double your battery and solar just to run CFLs, or 7x your battery and solar to run incandescents. That's just crazy. No, LEDs are not ugly light (more on that). Yes, the government forcing swirly CFLs is unfair, but LED is also winning fair-and-square because it's better.

You can get 12V LED lighting in all sorts of shapes and sizes:

• Kitchen lighting such as much of IKEA's
• "LED strips"
• automotive style 1156 bulbs
• off-road/driving floodlights (often too blue)
• 12V "RV" screw-in bulbs (not recommended, someone will try using them on 120VAC)

Be careful with your choice of color temperature and CRI when buying LEDs. A lot of the early or cheap LEDs had poor CRI and harsh color temperatures, and they got a bit of a reputation. These days you can get any CRI or color temperature you want.

CRI is Color Rendering Index, or how good the light looks to humans; aim for 80 or up (out of 100). Color temperature is how "blue" the light is. The traditional warm incandescent lighting is 2700-3000K (kelvin, weird unit, I know). 4100K is office fluorescent lights. 5100K is a cloudy day, blue-sky is 6500, and that sounds great when you're buying it, but it looks awful at night. Try to have all your LEDs be about the same color temperature.

Other loads

Make a very serious effort to find 12V versions of anything else you want to run. These days a lot of flatscreen TVs are 12V friendly. Boaters, RVers, tiny-house and VanLife people have good sources.

Inverting to make 120V involves a serious amount of energy loss. Even an inverter sitting idle has a fairly high power consumption.

You can't run them 24x7 or they'll destroy your battery. In fact, don't neatly install one. Leave it something you temporarily hook up in a tangled mess, so you'll remember to unhook it and put it away.

Don't overwork the battery

Both your batteries are lead-acid type. That particular type has a serious problem: it *really, really does not like being deep-cycled.** Deep-cycle lead-acids, like your Optima yellowtops, do better -- but they still will be destroyed by deep cycling, just will get more cycles before they do (on the upper range of the numbers I'm about to give).

• If you drain it dead, you'll get 5-30 cycles before battery death
• If you drain to 50%, maybe 20-200 cycles
• if only 25% DOD (using 25% of capacity) many hundreds of cycles
• 15% DOD thousands of cycles.

Factor this against the fact that lead-acid batteries typically fail anyway after 5-7 years. The upshot is, depending on your usage, you may need a larger battery for this system to make sense. Or...

Other battery types

You may think "Wait, my laptop/iPad/phone doesn't have that problem!" Correct. But before you start salvaging 18650's out of laptop batteries, lithiums have a different problem: spectacular battery fires. To avoid that, you need to build battery packs carefully and include a protection circuit - many people are doing this for off-grid / home-power. There are lots of instructionals out there, some not so safe.

There are more traditional battery types such as the famous NiFe "Edison battery" or its brothers NiCd or NiMH. But you're not going to find those on the cheap.