Is the sustained Medieval-Rennaissance divide between Westeros and the Free Cities realistic given their geographical proximity and commercial interaction? Are their any similar situations in history?

It’s absolutely realistic – the Renaissance as an intellectual and cultural and economic movement overlapped with what we think of as the Late Medieval Age, which ran from 1301 to 1500. Michelangelo was 12 when the Wars of the Roses ended; Leonardo da Vinci was born two years before they started (and a year before the Hundred Years War ended) and outlived them. 

Edward III fought the battles of Crecy and Poiters with gold borrowed from the Bardi and the Peruzzi bankers of Florence, and his failure to repay in 1345 was one of the reasons why, a generation later, Contessina de Bardi married Cosimo de Medici, who used her family’s reputation to help make himself Florence’s “king in all but name.”