While not an essay, the book Stepmonster is often recommended in our community - one to read with your partner. It covers the origins of the evil stepmother myth, and delves in to the challenges stepmothers face in a blended family. and why they face them.
Many here have reported that they read it with their partners and got decent feedback. While my husband did finally get his act together, he did not respond well to the book initially. It goes into great detail regarding the bond that biological parents have with their children that is not shared by stepparents, and his only take away was, "Yes, I fucking KNOW. You can't love her like your own! I GET IT." Less than helpful. Although, that was just his initial reaction and after a bit of time to really stew on it, he softened his approach with me.
The only reason I mention his initial not-so-great take on the book is because your SO sounds a lot like my husband was. And even if your SO does have the same knee jerk defensive reaction mine did, it's a very helpful book for you to read. It may help you find the words you need to explain to your SO what is in your head without being defensive yourself.
A nine year old is hard to be a stepmom to if you are only just now coming in to this. I met my SD when she was four, and it took us six years to get it right. Now at 10, she and I have a solid relationship. And that's pretty much the average time line, five to seven years to really and truly "blend" the family.
Well that's a good thing, because otherwise I'd be advocating for you to jump ship :)
Take a look at our resources page, there are a couple of things you can look into. Stepmonster if you have not already read it, and The Disengaging Essay. These may help you get at least your feelings sorted out and maybe your SO will open to reading them as well.
I highly HIGHLY recommend this DVD: https://www.loveandlogic.com/stepparenting-with-love-and-logic also sign up for their emails, they have awesome tips.
I'm not sure where she's at when she's not with you, I assume, her mother's house. If that's the case, do not send any toys to her. Mother's are very sensitive to step mothers, and she'll take it as an insult that you don't think she can handle her own kid.
Also read this book, Stepmonster, it is amazing. It has helped me in more ways than I can begin to tell you: http://www.amazon.com/Stepmonster-Look-Real-Stepmothers-Think/dp/0618758194