... How exactly did they get there to fight over it, and why are there many more Bretons in Markarth than Solitude?
By the sea probably and there must be an entrance somewhere along the border. I've already found two entrances, or exits: one that leads to Morrowind, south-east of Riften and another one that leads to Cyrodiil, south-east of Helgen. They look like wooden gates. The road from Solitude crosses the border and leads to Jehanna; the path should be there, at the end of the road to the west.
http://www.imperial-library.info/sites/default/files/gallery_files/cyrodiillargelowrescr7.jpg
About Bretons in Markarth; people travel and Markarth is not that far away from the border.
