The Tinker and the Farmer's wife seems to be a scots version of the 'Farmer's cursed wife' or the Devil and the ploughman according to an internet search. I am a bit sceptical about this interpretation however I did collect a couple of versions of the Jolly Tinker from the Gypsy Folk. One of them had a 'Touch her if you dare' chorus. There is also the possibility it could be related to 'The Barley Straw'
The 'Buy his broom' reference is interesting in as much as it has a 18th century Cant meaning. To buy a broom is a Cant term to rob somebody and run away. To this day we talk about a brush with the law'
I have the distinct feeing that I am adding one and one and making twenty five unfortunately. This is the best I can come up with, and it's not very much I'm afraid.
Is your father's tune in common time or triple time it might help to track it down?