About a thousand watts (minimum) some would say.
The OP asked, "phantom loads can completely drain our battery if we are away for a few days. A solar trickle charger has been suggested to us but we have no idea what size of charger would be strong enough to keep the battery charge healthy."
You guys are really something, suggesting hundreds and hundreds of watts to maintain batteries in storage between camping trips. Maybe I missed where he said he was going to dispose of his generator?
My little 30 watt system keeps my batteries topped off for months at a time.