Just a curious question - have either of you taken parenting classes? Participated in a blended family support group?
Having joined a ready-made family at one point in my life, it's not easy to meld individual ideals toward child-rearing. And we struggled with the same when it came down to having one together. I was always too harsh, too strict, too this or that. But I also learned in marriage counseling that when it comes to having a daughter, it's a natural thing that Moms and daughters will butt heads a bit more than Dads and daughters will, just like boys will do the same with their Dads moreso than with their Moms. Add the dynamic of a new parenting figure into the mix, and the notion of "but I already have a Dad/Mom" of a child, and it can be a recipe for disaster.
Once I got past the emotional hurdles of my marriage failing, I invested in as many parenting resources as I could afford to acquire, in order to better myself, and give our daughter the best I had to offer. Dealing with the behavioral issues has actually become an effort to balance consistency in discipline (not necessarily punishment) with understanding what's really going on in HER mind that motivated the negative behavior.
I count myself VERY lucky to have added a new partner to my life who has picked up every resource I have in order to be flexible and do the same.
If you are able to sit down and say "Hey, I think we could BOTH stand to improve our parenting skills and provide a consistent environment for ALL our children," and he's receptive to that, then you have the opening you need to move forward. If the response is "but I don't NEED that," then I would say there are bigger issues to address.....