Like canihaveacoffee, we have stayed in CP 3 times (twice Sherwood, and once Longleat) and after the first (long-ish queue) arrival, we have arrived as early as possible (ferry involved so early lunchtimes), parked in car park, got out swimming gear bags and had a swim, with DH or I walking back to the main lodge to get our keys after 3 and then walking to the lodge. That is something that can easily be a family activity.
Once you have the keys, you can take the DCs and swimming bags to your own lodge, and then 1 parent can keep them corralled there (exploring, choosing beds, watching tv etc) while the other goes for the car.
One of us walked back for the car the last time, well after 4pm, and we did the big unpack then. Queues had eased considerably at the gate by then.
The previous time, we got really lucky and the lodge was right near the car park, and we got a space very very near the lodge itself, so we just walked everything in from the car park. And left a few bits to collect the following day, as it was so easily accessible.
The only warning I have is that on all 3 occasions, we had plans to leave the site and enjoy other things in the vicinity - and on all 3 occasions, the first time we turned on the engine of the car after unpacking was to repack the car going home at the end of the stay.
That said, we haven't been to Whinfell, and I suspect we'd be more likely to try and get out there. But we just find it so utterly relaxed and its such a rare chance for us to slow down that we genuinely just seem to find the world has stopped for a week.
We do a big shop once we are well en route - I know it was Morrisons for Longleat, and Sainsburys for Sherwood. I bring a few things already packed (my self catering/camping box has things like 5 dishwasher tablets, a 100ml refill bottle of washing up liquid, 250ml bottle olive oil, salt and pepper, a few seasonings we use very frequently, small roll tin foil, box of sandwich bags (for marinating things or saving leftovers as well as sambos), box of ice cube making bags, matches, couple of nightlight candles - as well as key kitchen implements as I always find some missing - corkscrew, 2 small sharp knives, wooden spoon, plastic tongs, measuring spoons, small metal cafetiere, 2 tea towels and a hand towel, 2 j cloths, washup brush, pair of silicon oven mitts etc). And possibly a couple of family favourites that we wouldn't necessarily get in the UK.
But then I stock up en route with tasty treats and easy catering options (at least 2-3 dinners, maybe an easy pasta dinner, an easy rice dinner, and meat for 1 BBQ - or whatever suits your family), at least a box of wine and bottle of gin, plenty of tonic etc. And a disposable BBQ/2 if the weather forecast is any way decent.
And resign myself to spending some money in the Park Market - it is more expensive, but not terribly so. So we usually end up getting croissants most mornings (it's where DD started to head to the shops on her own, doing the morning breakfast shopping in CP!), bread and lunch bits mid-week, some meat and veg later in the week, and if we run out of wine/crisps etc. Or we have found something we think is worth trying that we haven't seen before!
Our general aim is to self cater most meals in the lodge, but we generally expect to eat out for 1 meal per day on average - maybe 1 breakfast in the pancake house, a couple of days lunch and a few days dinners, and a few coffee/cake, icecream or beer/soft drink stops along the way too.