Start with location. Decide whether you want to fall out of your door and onto a beach, or whether you'd rather have a quieter, greener setting with the coast a short drive away. Both suit a staycation well; it's really about what kind of days you want to have. If you like the idea of an early walk before breakfast and a paddle before lunch, a coastal park earns its keep. If you'd rather cycle quiet lanes or potter around a market town, a park a little further inland can work just as well, especially if the coast is only twenty or thirty minutes off.
There isn't one single answer to how far ahead you should book, because it depends heavily on when you actually want to go.
Getting three generations away together takes a bit more planning than a standard family trip, but a holiday park set-up handles it better than most people expect.
Where it's worth spending rather than cutting corners is on the things that affect your actual comfort: a caravan or lodge with enough bedrooms that nobody's sharing a room they'd rather not, a park close enough to what you actually want to do that you're not driving an hour each way, and decent waterproofs and footwear so a bit of British weather doesn't spoil a day out. Saving money by squeezing into a smaller unit or picking a park purely on price, regardless of location, tends to show up as a less enjoyable week rather than a genuine saving.
Midweek arrival is the other thing worth trying. Weekend slots get booked up first, particularly for short breaks, so a Monday or Tuesday arrival often has availability when a Friday one doesn't. If your work pattern allows it, a midweek break also tends to mean quieter on-site facilities, since most other guests are working to the same Friday-to-Friday pattern you're avoiding.
Pace is worth planning around too. A multi-generational trip works best when the itinerary has some flexibility built in, a gentle morning walk that suits everyone, https://www.2cholidays.co.uk/holiday-parks/north-denes-holiday-park/ followed by an afternoon where younger children can do something more energetic while grandparents have a quieter few hours back at the caravan. Trying to keep every generation doing exactly the same thing for a full week tends to wear thin by day three.