Welcome to the Forum Woodhouse.
It is amazing how many people with special needs have a facination with Railways. You may well find that once you start taking one of your residents out that several of others might want to join in as well!
I would agree with TRP that the Middleton Railway and the Keighley and Worth Valley Railway would be worth a visit. Heritage Railways may well have more time for you especially at quiet times.
If you go to this site:
http://www.heritagerailways.com/
and then click on UK and Ireland Heritage Railways, you will find a list of the heritage railways in the UK. If you click on the name of the railway it will take you to their website for details of when they are open, special events etc. Current copies of the magazines "Steam Railway" and "Heritage Railway" give you similar information.
Start with the two we have mentioned and then it depends on how far you can travel. Obviously the National Railway Museum is not too far away and could be combined with a railway journey to get there.
Hope this is helpful and have fun. I'm sure you will. You might get hooked as well!
Best wishes,
John H-T.