This is such a sad thread, but I don't think you deserve to be bombarded with criticism. I think the emergency situation meant that since the death of your SD, all the decisions your husband and you had to make were reactive, having to be made in urgency and by default, you more than anyone else.
Firstly, it sounds like you agreed to adopting the child mainly as default because you didn't want your husband to do with his ex. This is an understandable decision, the last thing you would want is for them to form some sort of relationship again, which would have been inevitable considering the situation. So I expect you ended up becoming a mum even though it wasn't what you wanted just so that she didn't and worse, you had no time to reflect on the implication of this decision.
Then you probably assumed that this decision meant that you and your OH would approach the whole situation as a unit. Unfortunately, it seems that not only you didn't adapt to it similarly, but actually in very opposite ways. It sounds like he took on being a dad to that child immediately whereas you needed more time. It doesn't help that she is the child of his daughter who he probably loved, and there is likely some sort of unconscious desire to do better by this child than he did by his daughter, a chance for redemption. He adopted a grand child, you adopted a brand new kid, and that will have got you on different paths from the start.
Inevitably, it went downhill as the more he settled in his role, probably being self-rewarded by the growing love between them, the more you became resentful that it was taking away your need to get used to this little girl and built your own relationship as a mother with her.
I think the situation is in crisis and need sorting out asap. What support did you receive from SS? Have you received any counselling? If not, I think that's very poor practice from them.
Don't beat yourself up, don't hate yourself for how you feel, but do accept that you need help to sort it out and that involves changes from your OH as much as yourself. You need to go back to working together and a professional to help both of you understand how the situation has impacted on the other.
I really hope you turn this around and make it work as that child deserves parents who are united, and love her both equally.