RE: Anyway, for about $40, they list one of those solar
panel charge through your cigarette lighter deally
bobs.

That size panel will ONLY provide a small trickle charge, intended to simply
keep a battery up when the vehicle is parked for a long time.  And you
should be able to find the same kind of panel (size wise) for less than $40,
check eBay.
BTW, your Dometic refrigerator running on 12v is drawing about 8 amps or
better, would take a solar panel array the size of the top of your entire
rig (probably more) to just keep up with it during a bright day.