Homura letting Madoka make her own decision at the end of the TV series was a big deal, and I would like to point out that she basically spent the majority of the timelines preventing her from doing that (as Madoka states "I'm sorry. But I believe its because you've been protecting me for so, so long, that I'm the person I am now") although it clearly results in Homura failing to achieve saving Madoka the way she had being attempting to since the start. We see Homura, a character who has fallen so far and stagnated grow a little and accept Madoka's decision despite how painful it is for her to do so. I doubt we disagree here.
But then we get to TRS during the 2nd flower scene in the field when Madoka and Homura are talking:
Homura: You see, I had a really scary dream. In it, you had gone to a place so far away that I had no chance of seeing you again. And everyone else in the world forgot all about you. Only I could remember you in the whole wide world! I was so lonely and sad... But no one could understand how I felt. Surrounded by that, I started thinking my memories of you were things I'd just made up. And I began to doubt myself.
Madoka: That's a terrible dream, all right. But it's okay now. Because I'd never go alone somewhere so far away that I couldn't see any of you again.
Homura: Why? How can you be so sure?
Madoka: You know how wimpy I am. And because I could never bear to do something that would make someone as strong as you cry like this.
Homura: Then for you, that's something that hurts you so much you couldn't bear it?
Madoka: That's right. You, Sayaka-chan, Mami-san, Kyouko-chan, my dad, and mom and Tatsuya, and even Hitomi-chan and everyone else in our class. I would never want to go somewhere I could never see anyone again. Even if there were no other choice, I know I'd never have the courage to do something like that.
Homura: Right... you're right. Those are your honest feelings. And yet how could I have made such a stupid mistake? I shouldn't have allowed that to happen. No matter what I would've had to do I should have stopped you back then. Madoka, you should know that even when you know how much it would hurt you, you do have the courage to make that hard decision. When you learn there is something only that you can do, you're far kinder and stronger than you yourself know. Trust me, I know this.
It's a pretty sad and yet heartfelt scene at the same time. it describes her final actions pretty well, since its here that she expresses regret at allowing Madoka to make the choice she did at the end well acknowledging that she is the type of person that would be strong enough to make that choice. I have no doubt that it was during this scene that she acquires the motivation to do what she does to Madoka at the end.