It can be hard for brothers and sisters when you've got one that needs extra attention. Even with all the attention they get they can still feel left out. And guilt about it can leave us always trying to compensate and never quite managing it. I think your response to the letter is lovely and just the right thing to have done. When you chat with her let her know you understand that she sees you spending all this extra time with her sister and how that must make her feel and that you appreciate her being patient about it (even if she's not really that patient!) Could you think about her giving up a club to fit in some special time with her? But going on what you've written you sound like a very wise parent and I think offering you reassurance that your making all the right moves is probably more useful to you than any advice on what you should talk to her about... as I suspect you already know that part
Try putting in methods such as star charts for them, and target behaviours such as getting along, playing nicely together, talking nicely to one another, etc. At the end of the day or week if they have all their stars they earn a reward. Feel free to contact me if you want more advice.