It's hardly cutting edge technology. I'm a Cali owner but the technology for charging batteries through a split charger is the same and has been for about the last century or so:
The battery should charge from whatever generation source regardless of voltage rating but only when the battery charger detects less than fully charged to prevent overheating.
Stop/start should not affect it in any way at all.
The engine generation source, if the same as the Cali, will only charge the battery to around 90% full. This is because to achieve 100% the last few bits need to be trickle charged, something that can only happen with mains supply.
To preserve battery life the battery should be charged to 100% regularly, at least monthly, achieved by leaving the vehicle on mains charge for 24 hours once a month.
Any failure to charge outside these parameters is a service issue that if the vehicle is within the warranty period should be performed under warranty. The dealer needs a good kick up the posterior if he is not trying to resolve this situation urgently.
My last Cali had an intermittent problem: It would charge quite normally but in warm weather trip out on mains charging if the fridge was being used, and not restart without being unhooked and hooked up again. Engine charging was fine. It was eventually traced to a tiny failure in the wiring loom that caused a break in circuit when it got very warm. It took VW ages to sort but not through lack of effort and with involvement of the customer Care director who found a replacement vehicle from somewhere. I'm saying this not to wave a flag for VW, some of their dealers are dire, but just to illustrate the sort of focus MB should be having in sorting out this problem for you.
You should not need to think about charging or switching things on and off. The vehicle is designed to deal with those things for you. If you have to think, and worry, then the vehicle is not doing what it is designed to do and the responsibility to sort it lays firmly with the dealer.
