Thats really good you have been doing work in that area. Right at the moment, she is trying to get control of her life to make her life better, and that will include trying to control the conversations. She will probably not be in a place where she wants to really talk to you for quite a few weeks and thats ok.
Your job is just to try to make the conversation calmer and relaxed between the two of you. This is the validating part people talk about. First, try to talk as least as possible and just listen. And start smiling and make sure your voice is always as polite as if you were speaking to your neigbour!!!
Come up with several lines you feel comfortable with when she pauses, such as "yes, that makes sense" or " I can see why you feel that" A couple of them should work better. If things get heated, how about " I would like to think about this, lets drop this issue for today". And then have a couple of other light topics you can move the conversation to, such as "weather etc" Then you will not feel so flustered when you talk to her.
I would also suggest goggling "effective relationship communication" or similar and reading up as well.
