Sorry for necropost, but someone claims that even April calls him Father
I checked the longplay of "Geki kame ninja den" on YT (becuase i don't have a console to play my copy of this game) and i saw two times that April calls Splinter her father (as Otousama)
The first being before Level 3 starts and later during the ending
https://www.youtube.com/watch?v=XCRJ3ZJnXhs