Not a motorhome owner myself, but I run a fairly sizeable off-grid setup for a garden office so I've picked up a fair bit about battery management in low-light/low-input scenarios — and the physics are basically the same problem.
The short drive issue is brutal in winter for a few reasons:
- Alternator charging is inefficient for lithium unless you've got a proper DC-DC charger (B2B) in the circuit — a basic split charge relay just won't cut it
- Cold temperatures hammer your battery's acceptance rate anyway, so even if the alternator is pushing amps, the battery may not be taking them efficiently
- Short runs mean the alternator barely gets up to full output before you've parked up again
If you're running a lead-acid leisure battery, honestly it might be worth looking at whether lithium (LiFePO4) would help — Fogstar do decent cells at reasonable prices. The charge acceptance on lithium is dramatically better, so you'll get more usable energy from those short sessions.
Also worth checking: is your B2B charger (if you have one) actually sized correctly? A lot of people fit a 20A unit when a 40A would make a real difference on a 20-minute commute.
What battery chemistry and charging setup are you currently running? That'd help narrow down whether it's a hardware fix or more of a usage pattern issue. Curious what others on here are doing to bridge the gap — solar on the roof presumably helps in summer but doesn't solve winter shortfalls.