Great idea about bringing your own needles! I'm sure you read her right, that she was frustrated-- but she also agreed to meet you for a second time! So it sounds like she's willing to try again.
I think that's a great idea, to cast on for her (and knit a few rows so she's got something to hold on to), and try the rhyme. If she can't manage to get the entire stitch done, then just one step at a time:
1. Have her insert the needle into the stitch 10 times.
2. Have her insert the needle and then wrap the yarn around it 10 times.
3. Have her insert the needle, wrap the yarn, and then pull it through the old stitch 10 times.
4. Have her insert the needle, wrap the yarn, pull it through, and then take the old stitch off of the needle 10 times.
It will help build her confidence, which has probably taken a beating since the stroke.
I'm sure you were doing this anyway, but I would keep the praise going all the time. People who are frustrated imagin other people are with them, too, even when they're not, so if someone in that position senses the littlest bit of frustration in the other person, they're going to absorb that times 10.
As in all situations such as these, the helper gets as much out of it as the helpee! Keep us posted, this is a great thing you are doing!