Mine are 5 and 7, so I'm struggling to remember what a 19 mo old is like! So do ignore these if not applicable:
Seaside! - Redcar can be entertaining. My boys love the cliff lifts at Saltburn and watching the surfers, and the little train (don't think it runs in winter though).
My boys love watching the watersports at the centre up there ... I can't remember exactly where it is, somewhere near a retail park just off the A19 coming up to M'Bro.
If you have a back-carrier - climbing Roseberry Topping (near Great Ayton) is fun. And Suggitts ice creams and Petches Pork Pies in Great Ayton are to die for
I know how much you like trains - the Eskdale route from M'bro down to Whitby is stunning, and Whitby is great any time of year.
I guess at that age, they are pretty happy to go along with whatever you like - you don't have to work around them. So what do you like?