Right, so I know this is the motorhome forum and I'm usually lurking from the static caravan corner, but hear me out — I spent three winters living mobile before I planted myself on a site, and the short-drive battery death spiral is exactly what drove me to rethink everything.
The problem is brutally simple. Your alternator barely gets the leisure battery above 50% on a 20-minute school run errand, then you're drawing from it all evening. Repeat for a week and you've quietly murdered a perfectly good battery through chronic undercharging.
What eventually sorted it for me (before I went static) was a Victron Orion-Tr Smart DC-DC charger rather than relying on a split charge relay. The relay is essentially useless in this scenario — by the time the voltage difference triggers it meaningfully, your drive's nearly done. The Orion actually charges the leisure battery properly from the alternator, even on shorter runs. Made a noticeable difference through a January in Northumberland.
Some people swear by adding a small solar panel on the roof to compensate — even a 100W Renogy panel will drip-feed enough to offset the losses if you're parked up during daylight. Not glamorous, but effective.
The other thing worth checking is your battery's actual state of health. If it's more than four or five years old and struggling in winter, it might just be on its way out regardless.
Anyone running lithium leisure batteries finding it's any better with the higher charge acceptance rates? Curious whether a Fogstar or equivalent actually holds up noticeably differently on the short-hop charging front.