Larry was originally married to another woman (Kirsty's mother), who had died, so he re-married to Julia. He was most caring about his daughter Kirsty. He had a tough life and all he was trying to do is keep his family together. His wife Julia cheated on him with Frank and was secretly helping Frank get more blood by bringing men to the house while Larry was at work. Larry hates watching himself bleed and when he cut his hand by a nail on the wall by trying to push a mattress up the stairs, he thought he was going to faint or throw up. For kindess and caringness to his family, he gets in return a wife who cheats on him with own brother Frank, then killed and his skin taken by his own brother.
In Hellbound: Hellraiser II, Frank Cotton appears to Kirsty, claiming to be her father and in Hell, which sets forth the chain of events in the movie. She finds Frank and defeats him, but never finds her father. It's never mentioned in the movie, but the best assumption for why she never found him was simple: Larry Cotton was a good and loving man who, after dying, would have gone to Heaven.