I strongly recommend option #1 - Use a charge line from Motorhome to your towed vehicle.
Will be sooo much cheaper and easier in the long run. No extra battery to have to purchase, wire in, keep charged when not in use, etc. Let the Motorhome's 12V system keep your car's battery charged so it can run the brake system, and don't worry about it.
I did this with the last two vehicles I towed, and it worked great all the years I towed that way. Just plug in the red 6-way cable and forget about it. Nothing fancy is needed, either, just have to make sure you put a fuse on the charge wire right before it goes to your battery.
Current towed vehicle (Jeep Wrangler) does not need this, so did not wire in a charge line when we set it up to tow. The last two did, though, and if the situation ever changed and I needed to keep the battery charged, would be very easy to run the wire to do such.