He and Margaret have children Alan, Lisa, Eddie and Aoife Mulholland.
Mulholland expanded the business, and by the early 21st century owned ten betting shops.
Influenced by Garret FitzGerald, Mulholland stood for Fine Gael and was elected with a large majority for the city's South Ward in 1985, becoming mayor the following year.
He was again elected mayor in 1996, and oversaw occasions such as a civic reception for three-time Olympic Gold Medal winner, Michelle Smyth, leading Galway's highly successful business mission to Milwaukee and Chicago.
He was host to Chief Garry White Deer of the Choctaw Nation on his official visit to Galway; one hundred and fifty years earlier, the Choctaw Nation had sent famine relief to the people of Ireland, despite at the time being in the process of banishment from their homelands.