Well the situation happened. Went better than I thought but still could have gone a little better. I don't think I could have handled the situation without reading peoples advice here and the books I was suggested to read.
When she came into the house, I thanked her for coming down and offered her a drink. She quickly went loo and came back, her first comment was "I like how the taps have different tops". I wasn't sure if she was having a small moan but I replied with thanks.
I told her I would say what I need to say and if she wants to add then she can at the end. She agreed. I mentioned everything I said in update 2. Then when it came to her telling me her problems with me, it was clear the clinking of the glasses was not the issue at all.
She stated many times how 'rude' or 'unpolite' I was for not clinking the glasses. MANY times, from what I learnt with the book I stated "I can understand why you might feel that way but that was not my intention" She then asked 'why' I didn't want to clink the glasses, I ended the conversation by saying "I can understand why you want to know but it isn;t important, what is important is I will do it in the future and we can put this behind us".
She tried to frame that I shouldn't have walked away when she swore at me and we should have worked things out. I stated again that I could understand why she would want to work things out but If someone swears at me, I leave, which is why I said next time don't swear but talk about the problems.
She then moved onto her next problem which caused the whole clinking glass drama. Her problem with me is that I don't talk to her enough because Apparently I'm only talkative when I have been fed or haven't had much sleep so she finds it difficult to get to know me better and when I do answer she said I only respond with one worded answers.
I slipped up in frame a couple times but got it back. I agreed I am tired and don't intend to fall asleep at their house so instead I will only stay for a couple hours. I disagreed about being hungry makes me not want to talk more. I also agreed that when I am tired I don't talk much but there is nothing that can be done about that.
She then tried to suggest even when I am not tired I don't talk either, which is half true. I explained that she may like to talk a lot about herself but I don't so if she wants to know more about me, she needs to ask more specific questions.
She wasn't happy and said that she wants to get to know me more, and can't if I only answer one worded answers. so I explained if she wants to get to know me more then she has to be more specific and that I can't change who I am. I did note to myself that I could try make an effort to be more receptive but personally I don't care if she gets to know me or not, so if she wants to ask it's up to her. She tried to frame me as it is wrong that I am the way I am, so I framed her that she is the only person who has ever said that, which is true. She then had a moan saying I must think she is special so I reply with a typical "I can understand why you might feel that but I don't" All learnt from the book. I wasn't being any different to her than any other person, she just didn't like that I wasn't as talkative as her but the weird thing is that her mother is exactly the same as me.
Anyway, she got a new car and wanted to show that off. Went on her merry way. She seemed happy by the end of it, but I could tell she wanted to change the way I am in conversation.
I am new at all this and I'm sure I could have handled it better but at the end I reached all my goals. Made peace with the mother in law. Made it clear to never swear at me again and I don't tolerate it from anyone. Accepted to clink the glasses in future. Wife is happy and even tried to stick up for me when I lost frame which was nice of her but reminded me I needed to get back on frame.
Thanks for everyones help, I couldn;t have done this without all the positive comments. I have a long journey of reading more material as there is still plenty to learn and practice.
TLDR: Achieved all my goals and went better than I expected.