I think Hazumu's dad is getting the short end of the stick, since we aren't Japanese. I think he's basically trying to spoil Hazumu, and doesn't exactly realize that his attempts are... well... sick.
He is also dealing with her sex change and is trying to act like a Japanese father would with his young daughter, although he's missing her age by a few years. I don't think it is odd for JP dads to bathe with their young daughters and perhaps this why he is acting so bizarre. Then again, Hazumu's parents have been pretty much playing out an Osaka comedy routine. (The slap "what teh heck???" thing, if you remember Azumanga Daioh, is typical, stereotypical Osaka-brand humor.)
Or he could just be a perv.