Very few people in the world take criticism well, or take owning up to their own weaknesses and misdeeds well. Your husband is probably feeling very defensive (I know I would in the same situation). Do you talk with him, and reassure him that you’re not trying to make him the bad guy, that you are just trying to make your marriage better? I don’t think you can reassure him too much at this point. Maybe this is what Dr. Phil is always talking about, when he says you have to give to get in a marriage (to paraphrase). If you can find ways to really support your husband now, maybe he will find ways to work on his weaknesses for you, if he feels safe.
Which is not to say that it’s your responsibility to fix everything. I’m just hoping to give you some perspective on what might be going on with him, that is causing him to drag his feet here and make untrue accusations.
Regarding your daughter - I have a feeling (based on not knowing any of you at all ) that she will come around as you start to expect better treatment from people around you. I hope so, anyway. I’m pulling for all of you; if you have an 80% good marriage, with 20% bad, I hope you can work on that last 20% and not have to give up the other 80%.