Assuming you are refering to the three cities in Scotland and assuming they have to be passed in that order then I get 181km (using city centres not airports) passing over Banockburn-Perth-Dundee-St.Andrews-Leith-Edinburgh.
If they can be done in any order the Glasgow-Edinburgh-Dundee (or reverse) would be 128km and passes over Airdrie-Livingstone-Edinburgh-Leith and Buckhaven.
These answers are probable wildly out though as I found three websites with turn radius formulae/calculators and got three different answers!
As for the cow, simply plough up half the field before hand
