you are a toxic parent

I have a sinus infection, the cough of death, very little voice and keep coughing up a toxic substance, but that isn't the worst thing in my life.
two days ago after I asked the mother for space,  I got another text 3 hours later.

"last text and then I will give you as much space as you want.  As Twin told me to leave you both alone I assumed perhaps wrongly that she and you had talked and that it was a joint decision.  All I have done was try and get help when I was sick with a temp that was causing hallucinations (are you sure it was the temp mum) For obvious reasons this scared me but the doc reassured me that it was normal in the circumstances and told me to take more para which I have done, my temp is lower but i still feel very ill and am just waiting up til I get my tablets before going back to bed.  I thought that once the doc spoke to you things would improve, important sorry if i confused you with Twin. You must decide what you want , am i is to contact you again and if not is it because you need space or like twin have decided you no longer want contact at all.  I will do what ever you want not because I want to but because you ask me"

My response was that twin was being really supportive telling me that it was between her and mum and that I shouldn't take sides but keep contact.  But that mum was insisting I pick.  And i asked her agin to give me space which she agreed to.  That space lasted a total of one hour and then

"Your dad has denied saying or implying that I harassed him at the weekend and knows nothing of my supposed texts to Dad's Girlfriend which I still have.  She texted thanks for Nieces presents and i told her that i hoped they all had a very happy Christmas.  I said I had to cancel Nanny's visit amongst others as I was ill.  She replied with good wishes for my recovery and spoke of the kids enjoying the presents.  That was all! I assumed dad told you this but he says no. If not him it can only be dad's girlfriend, whoever did is lying and clearly has an agenda of their own. (last sentence makes no sense) Important detested by a"

My response was simply that I asked for space so why did you send me this

"sorry meant devastated by this! I have proven that I am physically ill and I totally deny the allegations, now you have has much space as you need"

I told her I had never accused her of anything, just asked for space, so she didn't need to justify herself to me so now I was really confused"

her response to that was take all the space I need.

Now I happen to know from Dad directly that she demanded to see the grand kids and that she wouldn't initially speak to him on the phone.  I also know that he hung up on her at least twice because she wasn't making sense.  The girlfriend also told us directly that the messages to the kids were weird and she couldn't let them see them.

Now dad isn't perfect.  Growing up he was as toxic as mum is with the really aggressive temper and he almost lost all three of us because of that.  His relationship with elder sister is still very fraught.  But he realised  what he did and tried to change.  He's far from perfect but honesty was never the issue with him and i trust what he says.  Mother on the other hand is proven to lie and bend the truth to suit herself.

And now I'm thinking that enough space would be 100 years or 10000 miles.  She may have been physically ill, but that doesn't account for her mood changes, accusations and lies.  How can I have a relationship with her until she seeks help for her dependency and mental health issues?  And why do I still feel like the guilty one