Here is an idea
Call a family meeting and say that you need this family to get along but you understand there has been some friction. To facilitate this you are going to do the following.
You will have a meeting with each person individually and ask what they want the other person to agree to do, and what they will do in return (eg your daughter probably knows she shouldn't say things like I wish my mum never married you, or you can't tell me what to do since you're not my dad etc). After this you will have another family meeting and arbitrate a discussion between the two of them where they compromise on what they agree to do to improve the relationship and what they want the other person to agree to do. And maybe even have some requests of you.
Once you have it all agreed, you will all work out what they will each do if they breach the agreement - they'll be things that involve them being nice to each other. For example if your husband breaches the agreement he'll take your daughter out for ice-cream,or do one of the chores she normally does. If your daughter breaches the agreement she will go with him to a sports game or something else that she might otherwise have rolled her eyes at, or do a chore that he normally does. The list of possible things will be agreed on so she doesn't think she can use it to do something you wouldn't normally let her do for safety reasons eg go to a party where the parents aren't home or go to a concert late at night etc.
You'll print all this out in a way that looks like a proper legal document (so your daughter might take it more seriously and it might amuse your husband so he doesn't feel so aggrieved by the whole thing etc), have them sign it, you sign as witness and you make a couple of copies so she has one, he has one, you have one and you stick one on the fridge or pinboard (lots of copies so she isn't tempted to rewrite it with different wording and pretend it was always that way).
That should remove the day to day conflict, and when there is some, they should quickly make up over the activities and hopefully might even grow a better, more natural relationship