The main options for these kinds of places really are Swinley, Bedgebury and QECP. Otherwise it’s a trip.
QECP is okay, though careful in the wet as it’s chalk.
Deer’s Leap hasn’t even been on my radar so not sure what that’s like but no one seems to mention it.
There’s bucket loads of quality riding outside of trail centres though around the SE, but for all weathered family riding it’s a bit more limited. Other options are pootles around parks. Windsor Great Park even which has a lot of things of interest as well as riding round the park.
Alice Holt maybe. It’s dull for a proper MTB ride, though popular with families. It’s not a trail centre, but you get people riding around. Like Bedgebury, it’s expensive to park there.
Surrey Hills has one Swinley style all weather kind of trail over on Leith Hill, called Summer Lightning. Though take care if it’s gentle family ride as there are some technical bits, and it gets steep and very rooty once it hits the original section.