Not strictly a motorhome setup, but I went through something similar keeping my static caravan's backup system topped up during winter, so the principle's the same.
Short runs in winter are almost pointless for charging — alternator barely gets the battery above resting voltage before you've arrived. A few things that made a difference for me:
- Sterling B2B charger — transforms what the alternator actually delivers to the leisure battery. Night and day difference vs a basic split charge relay
- Solar as a supplement — even a couple of 100W panels do something on bright winter days. Not much, but something
- Check your battery's actual state of health — I had an AGM that was quietly sulphating and accepting charge but not holding it. Replaced it with a Fogstar lithium and the whole system became more predictable
The real issue is that most factory split charge setups are designed for summer touring, not winter commutes. If you're doing 20-minute runs in December you're probably not even breaking even on parasitic drain.
Worth looking at whether a mains hookup top-up once a week is just the pragmatic answer for winter, rather than chasing a solution through the alternator alone.
What's your current charging setup? Split charge relay, VSR, or something more sophisticated? That changes the advice quite a bit.