Creative solutions to convince research dean that I deserve PhD candidature
I think you are focusing on the wrong part of the issue here. Trying to prove your attendance is not going to help you at this stage anymore. Bringing in others like the guest lecturers is only going to make matters worse.

Instead, here is the three main steps I suggest (plus a very important bonus step):

1) Apologize.

As you report having to leave a lecture due to anger after talking to her, I would almost take it for granted that your behaviour was problematic. Apologize. Do not attempt to justify your anger.

2) Express gratitude.

You mention that you feel it. Express it, and be sincere.

3) Detail (maybe in writing) how you have applied the lessons you learned from her.

While Steps 1) and 2) are just plainly proper behaviour, and will hopefully make her want less to fail you, this step is about showing that you actually learned what you were supposed to learn. Really go in depth here. This is the base for your case to be advanced to candidature. Be specific over what you learned and how you used it.

Bonus step: Given the overall dynamics of your story, it is completely unsurprising that the lecturer is female and you are male (that is making an assumption from having a wife that got pregnant). Examine whether you have an issue with female authority (the answer is probably yes), and search for ways to mitigate this. This will probably take you way longer than the two days that you have, but it is going to be a worthwhile endeavour.