Some TMNT stuff really isn't for little kids.
In the Mirage comics, April's father is first mentioned by name only after April for a time moved from New York to Los Angeles to live with her sister Robyn to look at her messed-up life in a new orientation.
Not much is known of O'Neil, only that he is a antique dealer who owned his own shop, "Second Time Around", and a proficient businessman. One day his daughter Robyn was born, but his wife could no longer bear any children. In his examination of a few things that he purchased, but had not yet sorted, he had found a strange crystal, O'Neil attached the crystal to a pencil and miraculously O'Neil's was able to bring his drawings to life. O'Neil decided to satisfy his wife's desire to have children, but all of his attempts to create babies broke into nothing, as he had drawn them with a pencil. Sometime later O'Neil tried again with an ink pen, the result did not disappear this time and grew into a young woman: April.
Nearly thirty years later O'Neil died of a serious illness (probably cancer) and bequeathed his entire estate to his daughters, he gave April his old antique shop (but by then it was already destroyed by the Shredder and the Foot Clan when they had sought vengeance on April's new friends, the Turtles). All his life he had the secret of her origin concealed from April, until she had to learn through a chain of dramatic circumstances that she was not a naturally-born creature, and only some time later with Renet's Help was she finally able to discover the truth. This realization gave April a severe emotional crisis, and she left her old life behind for a while to find a new meaning to her existence.