In the old days I could stick a hydrometer into the battery and measure state of charge, caravan was often taken to Mid Wales about 1.5 hours from home in North Wales, the old Lucas blocking diode never worked, but the relay did to some extent, using 65/0.014 cable both to caravan and to box in boot of car, a 60 Ah battery after starting the car would show a good 10 to 15 amp charge, and depending on car battery some times up to 20 amp.
So with a battery where fully charged was 1.260 starting at 1.200 it would reach 1.210 in caravan and 1.220 in the car, in dad's car boot over 6 days it would go from 1.200 to 1.245 that's 2 x 1.5 hours plus daily run to work, but only way to get it right up to 1.260 s.g. was to swap prime mover and slave battery over. However it was enough to allow us to watch TV for one hour a night. And easy enough to measure how much power in the battery.
However today we can only measure volts, at 12.8 volts the battery with no load or charging for an hour should be fully charged, however experiments have shown how a sulphated battery can take weeks to recover, seems odd but that recovery once it starts is quite fast, but we can't really measure how much energy has actually gone into the battery, and even with the narrow boat with 6 hours a day with engine running the batteries never fully recharged unless one could get a shore supply for a day or two. So if you wanted batteries to last, once a month you needed a shore supply.
So on leaving home caravan battery 95 Ah fully charged so trip to camp site does not really matter if it charges or not. All the 13 pin socket does is work fridge, and if switched on before leaving home full of food, even that does not really matter unless travelling for over 5 hours.
Even with a DC to DC inverter say 20 amp stage charging charging will only go to 80% as at that point charge current drops, and we simply do not tow for long enough to fully recharge battery, so best case for 5 hour drive around 65 Ah into a 95 Ah battery, but a 10 amp charger would still put in 50 Ah and less likely to cut out on under voltage. As to simple relay likely only 20 Ah however that is better than nothing, and enough to allow a few nights off line as long as once a week you find a site with hook up.
However a inverter generator say 2 kW will allow one to cook using microwave and induction hob, and vacuum the floor, and running for just 1 hour a day will likely replenish the battery just as much as a 5 hour move site to site using a voltage dependent relay. Add a small solar panel and you have as much as one could possibly hope to get with a DC to DC inverter.
Or so it seems?
And this is the problem, people are unwilling to say, I made a mistake, I bought a generator, solar panel, fitted a voltage dependent relay, a DC to DC inverter or any other device and it would not fully recharge my battery so on arriving home had to recharge battery from mains before I could take caravan around back of house with motor mover.
So nitty gritty what I want is if the last site is without hook up, and 3 hours from home, and I get battery down to 5% charge before leaving, for enough power to go into battery to run motor mover to get caravan around back of house, from charging times using fully charged battery and recharging after I need around 20 Ah of power. If I can't get that much, then alternative method is a charged battery at home. Or a caravan small enough that I can tow it to behind the house and not use motor mover.
What I don't want to do, is spend a few hundred pounds on a DC to DC inverter, then still have to swap batteries when I get home.
So a report that says went to Scotland, the battery would no longer work TV, travelled home for 3 hours (miles don't matter it's time that matters) and the motor mover got caravan up the curb and failed, or got caravan around back of house 40 yards and failed, or got caravan to back of house and in storage position around 50 yards. And I have a car with/without power saving charging, and am using a voltage dependent relay/10 amp DC to DC/30 amp DC to DC and caravan is 950 kg/1250 kg/1500 kg etc.
Living in Scotland and taking caravan to France sleeping on ferry so 4 hours to ferry and 8 hours once off ferry and one would hope any car charging system would put enough into battery to work motor mover when they get home. I however living in Mid Wales and now no passport am unlikely to tow for over 3 hours. Even before the car which switched off charging, I know with a voltage dependent relay 65/0.014 cable moving every other day, I was limited to around 1 hour a night TV, at that time no motor mover, at end of three weeks holiday battery was about flat. Without the charging from car would have only lasted a week. So when people claim their voltage dependent relay keeps the battery topped up, I wonder if we are living in same country?