Aberdeen to Kilmarnock is roughly 170 miles, by car 3hrs away
[in theory] and by train 4.5hrs with 2 changes.
British Rail site is http://www.railtrack.co.uk/travel/
click on timetable and enter details.
I`ve driven on the other side of the road when in the States and it is
amazing how quickly you pick it up!
Have a lovely holiday and happy hunting.