Yes, being cautious and guarded is good. This yo-yo behavior is worrisome.
For your walk, be pleasant and upbeat. Look good. Wear something nice. Don't get into R talks and if she does, just validate.
The only thing I have to say is that be true to yourself. I assume that you are joining her because you think you can walk with her and handle yourself emotionally. I think it'll be hard as wounds are recent and raw. If you can't do it, don't. No need to put yourself through more self-inflicted pain. If she's serious about MC and working on the MR, she will put in the effort. Remember, you are the prize to be won, not the other way around right now.
I will reiterate what Sandi says again - words, actions, and attitudes have to line up. If she is sorry and remorseful, then she has to buck up and do something about it to repair the MR and show humility as well. If you don't see all of those things lining up, I would be worried.
Also, take your time. There is no rush here. She may go back and forth, hot and cold, for a while. The key is that you stay put and straight and engage in self-care. Don't fall for any bait for fights.
Read up on the validation cheat sheet by Wonka. It has been a godsend to me at times.
