I haven't read the whole thread, but I've read enough.
I was going to ask if you were autistic before I got to the initial post mentioning it.
There is systemic discrimination against autistic mothers by authorities. Anyone who does not acknowledge and understand that should not be insisting "there must be more to it" than the OP says.
Inform yourselves: network.autism.org.uk/forum-discussion/widespread-discrimination-against-autistic-mothers-autism-parents
tbinternet.ohchr.org/Treaties/CCPR/Shared%20Documents/GBR/INT_CCPR_CSS_GBR_20656_E.pdf
I am autistic. My abusive ex went to family court about contact (originally, though his demands expanded). He got legal aid and I didn't.
Social services became involved. They decided I was emotionally abusive and neglectful. Their concerns were along the lines of my daughter sometimes having dirty nails. And they criticised me for answering the questions they asked me when she was in the room - was it some kind of test?! If I'd refused to answer they would have said I wasn't co-operating.
They put her on a Child Protection Plan which had no goals on it. So although I complied with what they wanted such as seeing a family support worker (who made my home stink of smoke and had nothing useful to say), there was nothing I could actually do to get off the plan.
They also recommended that she be sent 150 miles away to live with my ex.
The only professional involved in the process who actually knew my daughter was her forest school teacher, who voted against her being put on the CP plan. But everyone else present (who never met any of us before or since; they were just random representatives from the police, school nurse service, etc) automatically voted with the social worker (the first of three we had during the process, and who'd only been practising a year).
While she was on the CP plan, I wasn't allowed to leave her with any adult SS hadn't pre-approved (including a police check), because if they're on a CP plan your judgement is considered too bad to choose appropriate carers.
They only checked me, my ex, and my current partner. They said I could ask for friends to be checked so I could leave her with someone, which I did, for two friends, but they didn't do it. And you can't take the child to the meetings (not even to the building), so my partner had to take loads of time off work to look after her for court dates and SS meetings.
They also tried to tell me I wasn't allowed to home educate a child on a CP plan, which is not true, but the LA had put it in their policy. So then the education team got involved to assess my provision (which is over-stepping their boundaries, but I complied with that too).
They just left her on the CP plan until the court process finished, then downgraded to Child in Need, then left us alone eventually. Without me having changed anything about my parenting, because there was nothing wrong with it in the first place!
Fortunately we had a decent Cafcass officer who didn't agree with their recommendations, and the judge did not order what SS wanted.
But if not for her, or if there had been racism involved too (or more racism; there might have been some level of that as although I appear white, I am mixed-race and don't have a standard British name), I might well have ended up in the OP's situation too.