For the Lake District you may find this useful-
https://www.lakedistrict.gov.uk/visiting/things-to-do/family-children-activities
(pretty much the kind of list I'd have put together-I would add the South Lakes Safari Zoo at Dalton in Furness on the southern edge of the Lake District, and the Beacon Museum at Whitehaven on the western edge- it's a Museum but great activities for kids while the adults learn about the history of the tow which was once the 3rd largest port in the UK- these aren't on that list as they are outside the National Park boundaries. Whitehaven is on your way to Ravenglass which is on the list).
I don't know how long you plan to stay in the Lake District, or what your budget is, but we do have a Center Parc at Whinfell Forest.
It's just outside Penrith, 10 minutes from the M6, 1/2 an hour from Keswick, an hour from Windermere via Ullswater.
On Cumbrian local foods - get a good Cumberland Sausage- the real ones are wound in spirals, quite spicy- a straight sausage is not Cumberland whatever it says on the label, Rum Butter and Rum Nicky, Grasmere Gingerbread from Sarah Nelson's at Grasmere (always long lines outside, it's not gingerbread as most people know it. more a biscuit, some people say shortbread), Kendal Mint Cake, Sticky Toffee Pudding (must be Cartmel STP), try a good Tattie Pot (a stew). There are lots of good local cheesemakers and local micro-brewers. You will see English Lakes Ice Cream everywhere in the area- which is great but if you end up at Buttermere try the made on the farm ice cream parlour there. The spices and rum date from Whitehaven's trading days with the West Indies.
If you get the chance you must try the Herdwick Lamb- it's a very unique flavour of lamb, from a breed of sheep native to Cumbria- a great place to try that is Yew Tree Farm, Borrowdale- which Prince (now King) Charles often went to.
At Bassenthwaite (just west of Keswick) there is also a distillery. If you go there you must also go to the cafe at the former Bassenthwaite Lake Station. I'd go there rather than the Bistro at the Distillery. It's in the carriages from the remake of Murder on the Orient Express. Really good food, especially their afternoon tea.