My kids are young teens so we will be doing some hill walks - Catbells, Latrigg and Walla Crag all sound like they would be okay. I also like the sound of the railway walk
If your kids are teenagers, they'll be up and down Latrigg in about 30 seconds - much better off going for Skiddaw or Blencathra. More challenging, yes, but much more rewarding. Catbells and Latrigg really are for little ones, as entry-level fells!
I wouldn't recommend the railway walk during the school holidays as it's rammed with scooters, bikes, dogs, etc to the point where it's impossible to get anywhere - and there are also no views either. I don't understand why it's so popular tbh, unless you have a toddler on a scooter to entertain. If you want a low level walk, you're much better off either following the near side of the lake to Friars Crag and beyond, down Borrowdale, or else going on the other side of the lake through Portinscale and following the path to Grange.
Also remember the railway path is the route of Keswick parkrun, so avoid it at 9am on a Saturday!
Buses are really poor in the Lakes, unfortunately. Driving to Ambleside is going to be much easier than sitting on an (irregular, slow, expensive) bus for an hour. And if you drive you can also stop off in Rydal or Grasmere on the way back for the caves and walking at Loughrigg.