It's been a while since you've posted this, but I'll respond anyway. :)
My grandfather is the son of Lillie Mae, daughter of Joseph M. Mulhall and Theresa Ann (Burch) Mulhall. My grandfather told me many times that he believed his mom's side was Irish, and that at some point, their name might have been O'Mulhall. I have done some research. There is a book "The of Irish Names", by Ida Grehan. It suggests that Mulhall originated from O'Maolchathail (Not sure if this is Gaelic?). Another book "Irish Families: Their names, arms, and origins", by Edward Mac Lysaght lists O'Mulhall, which may have also become Mulholland, then Mulholland. My Grandfather said that the family may be connected to William Mulholland, who was born on September 11, 1855 (in Belfast, Ireland). He was obviously a major person in California history. I haven't yet found any verification of this, but that's what I've heard.