Re: My wife says she hates my daughter
Yeah, it sounds like your wife wanted to take your daughter's mother's place and got upset when that didn't happen. It also sounds as though she's jealous of your ex, which is both understandable and rather silly at the same time. On the one hand, she was probably jealous because you and your ex shared a child together, and your wife didn't yet have that bond with you. That might have led to her feeling slightly insecure. At the same time, it's rather silly to be jealous of someone that you decided you didn't want to be married to any longer. Now, of course, I don't know the details of your divorce, and if it was something where you didn't want the divorce, then it would make it slightly more understandable that your wife might be jealous.
As to how to fix this whole thing, though...that's hard. At this point, it's gone on so long that your daughter is now frustrated and building resentment toward your wife and so even if your wife changed, your daughter might not. Your daughter is only 10, which means she's still fairly immature, and as children will do, she's likely to hold on to her resentment and hurt feelings.
There are so many suggestions on this forum for marriage counseling. I think perhaps that's what your wife and daughter need. Not marriage counseling, exactly, but some joint counseling for the two of them, where they can get their feelings heard and discuss things but with a neutral third party there to keep things from getting out of hand. You can't be the referee, because they will each think you are on the other's side.
And honestly, while I doubt that your wife and your ex-wife will ever be friends (it happens, but it's very, very rare), getting them together might not be such a bad idea. If you can get them together, and get them talking, perhaps your wife will see there's nothing to be jealous of, and if she gets to know your ex, maybe she'll also back off a bit on demeaning her to your daughter.