Being a step mum

I have a 3 year old step daughter and a daughter of my own on the way, my partner gets his daughter every Sunday for a couple of hours and baths her before he drops her off but he cleans her with cotton buds like goes right into her ears and she screams cause it obviously hurts her, I don't say that you aren't supposed to do that because it's his child but things like that I don't want him to do with our daughter, I love my step daughter but I know my place and I just wanna know if any one else has experience of this?? My partner is very stubborn and I can imagine him saying 'I do it with Sophie (my step child) and she turned out fine'