Thanks for reponding to my posting. I don't know anything at all about the Scottish Muldowney but I may be able to help you in your search of their roots in Ireland before leaving for Scotland.
My particular line begins in Co. Mayo, Ireland then to New Jersey, then Philadelphia, PA. Before Mayo they probably lived in Kilkenny. My g. g. grandfather PATRICK MULDOWNEY (probably born in the 1820's) was married twice. I only know the name of one of the wives...MARY HIGGINS. Between the 2 marriages he had 22 children. Your Thomas could be one of them or even a brother or cousin of my Patrick.
Several of us Muldowney descendants are working very hard to find the family origins. We've had good success so far. I'll contact several to see if they recognize your info.