I remember your original thread and posted on it then. I really feel for you. This is one of those cases where no one is at fault (save the XW) but someone is going to end up suffering. At the moment it looks like you. 
The parenting side of things and equal treatment of all DC is something that can be worked on and improved. Your DH needs to understand that far from making life easier on your DSD if he relaxes the rules to begin with while she adjusts, he'll just make her feel unsettled as time goes on and the boundaries change. You need to sit down together and really, really talk this through until you're in complete agreement as to how you're going to handle things. Then involve your DSD and discuss it with her as well.
The animal/allergies side of things is far more difficult to deal with. As far as I can see, there are only two likely results: Either you learn to live without animals, or you and your DH separate so that you can. I can completely understand why neither of these would be acceptable to you. It's not as though you knew you had a DSD with allergy issues when you got together, and we're not just talking about a family pet here, we're talking about a whole way of life that you're being asked to change.
That said, the only alternative to those options is that DSD doesn't live with you. If it's not possible for her to go back to her mother (not that she sounds as though she should anyway, poor child) one alternative would be for DSD and your DH to live somewhere else temporarily while you throw everything you've got into seeing if you can gain enough control over her allergies to at least have some animals back with stringent cleaning routines. THere's no guarantee that will work, of course.
Please try not to fall into the trap of making your DH responsible for this situation. He isn't. He didn't know he had a DD, let alone one with allergies, when he met you. Whatever he does here he will fail someone - either his DSD or you and his DS. It's an awful situation for him to be in. It's not his fault anymore than it's yours or your DSDs. It's just a truly shitty situation and one that doesn't necessarily have a solution.
I think you have some hard thinking to do about whether your relationship is worth the sacrifice of your complete lifestyle, because in effect that's the decision you're going to have to make. In an ideal world, you wouldn't have to choose of course, and you're only in this situation because of the selfish actions of your DSD's mother. But your DSDs allergies - which aren't her fault - have made it so that you do have to choose. I'm so, so sorry. 