Am I the problem?

[Rhia91]

Okay, this is a long one. But it's got to the point where I am at a complete loss on what to think. And I need clarity for my own sanity!

Okay so for context I have a little boy who has autism. He's quite challenging at times and everyday is exhausting. I don't have any kind of support network, my mother looks after him for a few hours on a Saturday to allow me to shop/catch up with work etc but this is the only kind of support I have.
Okay so the actual topic now! I asked my half sister for some help with forms last year while going through a particularly stressful time of EHCP's, DLA forms and court mediation demands from my ex partner. She ignored my messages, only replying when I said I had sorted it another way. Her reply was quite rude and abrupt and I decided I'd had enough of people getting stroppy with me when I had so much going on myself. I distanced myself from her.
Later in the year she had a cosmetic operation on her toe. I didn't immediately think to message her to check in as I was dealing with a lot. She took great offence to this. I heard of her annoyance through another family member and decided even more resolutely to stay away.
Our mother was due to babysit my youngest son while I attended a work event. The sister got extremely annoyed as my mother was at her house making her dinner at the time. An argument took place over the phone to which I ended call. Mum then unknowingly called back and I heard My "sister" airing some very insulting remarks about me. I decided I didn't particularly want to speak to her again.
Mum feels caught in the middle as us sisters don't speak anymore.
I was at my mums house the other day and the sister turned up. I left very rapidly so as not to be in the same room as her. I am now being branded the childish and problematic sibling even though she was the one that then stormed out the house and shouted abuse at me in front of my small child.
Everyrime I broach the subject with My mum I get called 'crazy' or told "you need to speak to someone, your mental". I'm finding the remarks are really getting to me as I've had these sorts of responses for years from family members.

Am I crazy? Am I the childish one?

Just carry on avoiding. She sounds unhinged

We can't choose who we share DNA with, but we can choose our friends and family. I think you avoiding your sister is to minimise conflict. You left, and she proved you right because her reaction was to shout and cause a scene outside. I would not want to be around that and my child definitely wouldn't be.
However, I also have concerns that your mum is okay to call you names like 'crazy' with this situation. That is not deescalating behaviour, that is choosing sides.
Obviously I understand the support your mum provides with your child, and the need for that as a single parent is important. I would just not tell mum much, keep it to pleasantries and if she brings up the sister thing say it is best we don't discuss it and agree to disagree.
I hope everything else with ex, etc, calms down as that is a lot of stress with big situations at one time in your life. I'd consider speaking to the doctor about therapy as it will help you work through it and give you a safe outlet to offload.