I’m sorry to be negative but as someone who grew up in Whitehaven, I agree with other posters. It’s an extremely insular town, people are set in their ways and the general mindset is v backwards (people outwardly voice opinions that haven’t been acceptable since the 1970s / 80s and aren’t challenged for it).
I think it would be particularly hard for you and your children to build a life as outsiders to the area, and being Asian. Unfortunately a lot of people in this area aren’t welcoming of people from diverse backgrounds. Obviously I’m generalising as some good people do exist, but most people with anything about them leave and don’t go back.
Job wise there is Sellafield and not much else. The wages there are inflated and it seems to be fairly easy to work your way up if that’s what you want. I’m not sure it’s a place for a new business to flourish - it’s pretty rundown.
In terms of things to do, you have the lakes in driving distance but nothing in terms of culture or activities and opportunities for children. It’s fairly cut-off, a couple of hours from any decent-sized city and a lot of the way of life is still reliant on word of mouth and cash transactions.
Other than the harbour area, the town is run down, and some of the estates you wouldn’t want to set foot on. If you’re determined to move to the area, look at some of the nicer towns in driving distance like Cockermouth, Keswick, or further afield to Windermere. Having said that, those places are prettier but still aren’t particularly welcoming to outsiders.