his parenting

My partner and I have been dating for 2 years. He is my first everything. However although this is unrelated, he had unprotected sex with his previous partners and ended up giving me hpv. Not an issue because we are working on it together but this gives context.
He also has a 5 year old daughter. Cute as she is her behavior is very inappropriate. She continues to curse and act out. Not only that but her behavior is really the definition of inappropriate. For example she'll tell me that her dad tickes her peepee (I talked to him about that) or she'll come back from her moms house and tells her dad she misses him and his peepee 😳. My partner is constantly getting kicked out of the gym because the kids club would kick his daughter out for trying to kiss boys, pulling her pants down, grabbing people's butts and cursing. 
One day I will be living with this man and the step mother of his child so i suggested he does not buy her things when she misbehaves because I noticed he always does and think that's why she doesn't view her behavior as bad. 
Today for example we got kicked out of the gym becuSe of his daughter. We walked to whole food together to buy a few things and she picked out a card wanting to buy it...he buys it for her! I'm so annoyed because this is consistent behavior from him as an adult! I believe he should have said no you are not getting anything because you cursed at kids club and you should not be cursing. He could have bought the card in front of her and not given it to her and explains why and tells her she'll get it when she behaves 
I don't want to have to tell him how to parent his child but I honestly think he needs help in that department. I do not think I can live with him and his daughter in the future if she is not taught and shown throw reinforcement what is appropriate and inappropriate behavior. Should I tell him this? If so how exactly? 
With all that we have been through I really feel like he should work and focus on his parenting. He gets offended when people bring it up and says he disciplines her but he doesn't he just Spanks her which I don't think works. If I stayed with you despite everything can you please return the favor and teach your daughter right from wrong so I can come into your lives smoothly rather than irritated and annoyed and looking for a way out?