Your mom is narcissistic and kind of an asshole. I'm sorry, I know people don't like hearing that about family and especially parents, but unless I'm missing some important context, this letter is messed up. This letter is like the introduction letter from Emotional Manipulation 101.
You said you want to be able to be the caring, loving and sensitive person you have suppressed all these years and by admitting the truth to yourself you will be able to be that person, but so far you have not shown any of those attributes in the letters you have writen to me
In addition to
I'm certainly not feeling the love from you at the moment. // Consideration has never been one of your strong points, perhaps it's time for you to think about changing that.
Is a straight up attempt to get you to get you to distance yourself from being trans, or at least, for her to distance herself from you being trans. You basically said you want to be more emotional and empathetic, and she's saying that by virtue of being trans and trying to treat that, you are the opposite of those things.
It seems like she knows you're caring, though, because of how much she's trying to play on that to get you to put up with her bullshit. She hasn't given a moment of thought as to what you're going through, or how difficult being trans is. This letter is all about her and how difficult you're making her life.
Your friends and colleagues who have accepted your identity so easily can do so because they have never loved you as long and as deeply as I have
This is straight out of an abusive relationship. It's kind of hamfisted, but she's saying that people who care about you don't REALLY care about you, and that her love is more "pure" or whatever. That's an attempt to isolate you from influences that contradict her feeling on trans issues.
If you aren't down to mail her a picture of your middle finger, I'd just write a cordial letter about how this is something you've been struggling with for a very long time, that it's not fair for her to be making it about herself, and that you wish her the best and that you'll give her the time she needs to come to terms with things.