I think that as you are under an hour away @Heyhihobye, that it could be worth it, but I'm not sure how much fun the children would find it, especially the 1 year old. If your youngest uses a pushchair you might want to check wherever it is that you intend to visit, as since I had to use a wheelchair, some places - a lot of places - were too difficult for me to negotiate. That was because many curbs, and steps into shops, cafes, and restaurants, are very high, and along with some cobbled roads - in some of the town centres - it was just too difficult for me to manoeuvre. Of course a pushchair is much lighter, as is it's occupant, so they could be lifted into many of the type of places I mentioned.
The only activity that I can think of at the moment, and that you may all enjoy, to a lesser or greater extent, is maybe a passenger boat ride on Lake Windermere. If you want to do that, Ambleside would probably give you the best choice. (Some of the other lakes also have passenger boats)
I think that it would also be a good idea to research beforehand any free childrens play parks, and maybe - if the 9 year old doesn't mind, have a cuppa and a snack at a childrens soft play, for the younger two? If you could find somewhere that had both soft play, and something like a childrens wall climbing activity, then that could make a reasonable place where they could all let of some steam!
Talking of steam, I have a feeling that there is also a pleasant steam train journey, but I think it is nearer to the West Coast, and probably quite south within the LD. But I'm sure that it wouldn't be hard to look it up. However, I found that when we were actually within the National Park, most of the roads are very windy - like a snake, rather than windy like a gale! - and, of course, they also had lots of ups and downs. I always loved that part as you could get some stunning views from the higher parts, but it does mean that if you want to visit several different places in the one day, the roads can make the journeys take quite a bit longer than you may imagine from the distances.
Personally, I would not have even attempted the LD if I didn't have another adult with me to help with three children, and you haven't mentioned whether anyone else is going with you. Of course you might have a much stronger constitution than I do, and a 1 year old, a 6 year old, and a 9 year old, might be a breeze for you, so please don't let any negativity I have shown, put you off if you have no worries about coping. I would just add that it probably wouldn't be a great idea to go if it is forecasted to be a rainy day... 🤭
Whatever you do with them next week, I hope you all have a brilliant time 😁