Hallmark, I did some digging there. The eldest son of Anthony and Annie Kelly was Daniel Kelly (1870-1948). Assuming this name carried through the paternal side - no sign of it on maternal side yet - I searched Daniel Kelly for Belmullet. Find a marriage to Mary Cosgrove in 1881 (record listed as 1882 online though) and he'd be only 10 years younger than Anthony roughly. Father deceased and listed as Michael Kelly, Shop-Keeper. I also noted Rose Kelly as witness on Mary Carey and Michael Ruddy's 1875 marriage - Mary Carey was Annie Kelly's sister. Assuming she then connects to Anthony Kelly, she would possibly be a sister-in-law. Indeed, her husband is shown as Michael Kelly, born c.1845. They themselves also had son Anthony.
Wrapping this up I suspect Daniel, Michael and Anthony were sons of this Shop-Keeper named Michael Kelly. Do you know how I could dig deeper here? He may have owned land or suchlike. Edward Kelly also shows up as a son of Michael Kelly - here a farmer - in 1868 marriage. Not sure if this could be same Michael.
This remains speculative to an extent of course!