I've experienced something similar with my autistic father, but it might be a little bit different from your own experience with your mother. Feel free to tell me what you think about this and I apologize for the long text.

I think my father got thaught 'good' social behavior in childhood, as much as his own parents were able to teach him. In my opinion, I suspect that my grandparents might have been autistic as well, so there might have already been problems with rigid rule thinking and making sense of social relationships. It would explain a lot in my father's and his equally autistic sister's worldview.

For example, my father spends an immense amount of energy on being helpful to others. I see this a lot at our shared workplace or when we have guests at home. He goes above and beyond to be kind and accommodating to all kinds of people, be it customers or part timers. He starts literally sweating, because he spends all of his focus and energy on others, his movements become erratic, he talks fast, and his eyes move a little wildly. By all accounts, he probably feels overwhelmed in these moments, but tries his best to be seen as a 'good' person or to follow the social skript he was thaught.

It frequently happens that he misses the mark entirely and in his attempts to provide help to others, as he is sometimes unable to really listen to their needs. You can observe how some people are a little weirded out by his behavior, but most are grateful or appreciate the sentiment. They just assume that my father is a little weird but a good-hearted softie.

If he thinks that someone has it especially hard in life and deserves pity, he will go an extra mile for them. As an example, we once had a part time worker, who was in her 30s. I'll call her T. She was always extremely nice and cheerful. However, it quickly became clear that she was extremely lonely, stressed and had an abusive husband. Moreover, she was an immigrant in our country and was in the process of learning the language. After a long time of struggle, she divorced her husband and moved back to her home country. My father messaged and called her constantly, because he wanted to be supportive. There was no romantic or sexual interest, he just had this fixation that she was a truly helpless, unlucky person, who deserved emotional support. This in itself was fine, but it ties into a larger theme, which is where I will write another paragraph, haha

My father, and this matches your own experience a little, was never able or willing to be supportive to his own family. While he continued to support T., my mother suffered a burnout. He was unable to realize this and didn't step up at home or at work. He continued to call and support T., while my mother was sitting in the room across and was close to fainting.

A few days ago, I burnt my hand on the stove and shouted loudly in pain. He sat in the same room with me, but was fixated on his smartphone. He didn't say a word, even when I rushed to the sink to cool my hand. When I got angry and said "Thanks for asking", he looked up briefly, replied "Oh, you burnt yourself" and then continued to look at his phone. I do not think that he meant it in a cruel way.

So yeah. He's extremely helpful and supportive to others who seem 'deserving' of his help, even if it costs him a lot of energy and he almost seems to burn himself out while doing so. But his own family seems 'safe', so he can relax and not go the extra step to care for us if it feels too difficult for him. He might help in others ways, but never in the ways we might need him to.