For a family, I'd suggest you rent a car if you can, it's more flexible, might even be cheaper and oh, there won't be delays.
I only drove there myself, but I know there are trains going to Windermere which is the centre(almost) of the lake district. If you can stay there for more than one day, do some hiking, there are so many places and viewpoint to take a photo from, mountains, lakes, birds, boats, etc. I can't think of any particular place to start with, maybe Windermere boat cruise around the lake is a good option.
I can't offer you any more advice since I've only been there once myself and haven't really spent enough time to explore the whole place, but hang around, someone will give you a detailed and satisfying answer, it's a very popular destination for many landscape photographers 