Creative solutions to convince research dean that I deserve PhD candidature I need your help please to suggest solutions to a problem I am facing during my PhD. My story is detailed below with the important events that are related to the story:

I just finished my first year PhD at the university. It has been a difficult year for me because I had a supervisor who left and another supervisor who left again. My wife had home sickness and financially I had my scholarship fund cut by 30%. 

Now, I came across another obstacle in my PhD. During our first year, we have to attend a generic research course and complete tasks to confirm our candidature. Although I attended all lectures and completed all tasks, the course lecturer who turned out to be also the associate dean of research at the university decided that I have not done them. Her proof is that there is an electronic feedback that I have never completed after each lecture which she used to confirm our attendance. She mentioned this rule at the start of her first lecture. Because I didn’t know about this rule and because also sometimes my phone was without battery, I was not able to complete many of these feedback. I may have completed two or three out of eight.

Later, I went to the make-up class and tried to talk to her to convince her that I have done them all but because of all the stress I had from my other PhD issues, I may have become angry in defending myself which I regret now. At the end, she decided that it is OK to leave and I can send her an email stating my story which I did. Later, she sent me an email telling that not only that I still have to retake all classes but also I have to re- do all tasks. I thought it was not fair because I have proof at least that I have done the tasks. So, I did not fulfil her request because at that time 1) I was partly not thinking straight , 2) I was also still hoping to convince her that I have completed the tasks , 3) I was thinking of switching universities and thought I do not need to do them

Later and after I got admissions from a couple of other universities, I found that my wife is pregnant and the doctor told us it is difficult for her to move to another city. So we took the decision to stay at my current university. So, I went back to the lecturer and sent her an email to inform me about any remaining requirements but she still insists that I have not completed them. In fact, she talked to my supervisor after my email and suggested to terminate my PhD. She told him that one day I came to class, ticked my name and left straight away. This happened when I tried to convince her once at the beginning of a class but I was not able to so I left the class in anger. 

Now, I have to stay at the university and she said I will not accept you just retaking the class. She told my supervisor that  I have to come up with creative solutions to convince her that I deserve the PhD candidature. So, I need your help please to suggest some solutions to her so she can be convinced. She is meeting me in two days to listen to my proposal.

P.S. , I really enjoyed her classes and learned a lot from them. I thought they are really helpful. In fact, she taught us how to file a patent and because of her I got inspired and filed one. She also taught us how to write a proper paper and now I am writing my 5th journal paper. I also learned how to do a better presentation at her class which got me to present at conferences where I won two awards. However. she is still not acknowledging my attendance at the lectures. 

I talked to other colleagues who attended the lecture with me and they all were happy to testify that I attended the lectures. Also, one time she brought three lecturers from the university in class to ask them about any problems we have with our PhD. So I told them my supervisor’s change story. I am thinking to talk to them to see if they would remember my question. I also have an email to one presenter after he finished his lecture to commend on him on his presentation which I can show her to prove my attendance. 

I am sorry for my long post. Appreciate all the advice I can get.
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.