To not give her a lift?

Yep exactly this. Do not give an inch to these people.

I'd agree. Or just say that you have a personal appointment and it's not appropriate to have other children along. And give no further details

Stop being a wuss and message back
“to clarify, I will not be giving x a lift home either today or at any point in the future and if X abandons her child again, no doubt social services will be interested to know why.”

These people are not your friends. Who cares what they think?

I would just be straight up OP, I think you’ve made a bit of a rod for your own back by making excuses rather than being honest. She’s obviously a CF so you need to be firm.

Do the other mums know your daughter has autism? If so I’d say “As you know DD has autism & she needs a quiet environment on the way home. Your child was disruptive which really upset her - I’m sure she didn’t mean to, but as such I can’t help. I tried to save your feelings by making an excuse about shopping but I realise now I should have just been honest. I’m sure you’ll understand and if you were in my position, you would put your own child’s needs first too. Some of the other mums seem keen to help, perhaps they can give your child a lift?” Surely there’s not a single parent in that group that could argue against you putting your own DD first!

If they don’t know about DD having autism, and you don’t want to bring DD’s needs into it, then just say in the group: “To be honest, it was a bit of a shock to have that thrown on me in the moment, (name of parent). Do you have the right number saved for me? I never received a message to asking me if I could do it or minded. It made me really uncomfortable dropping your child off to a house with no parents at home if I’m honest too..” - again, it’s a bit more confronting but I don’t see how anybody can argue with that. The other mums might not realise you were never asked directly, in which case it might look like you’re backing out after offering only to do your shopping instead. I’d make it clear that’s not the case!

Tell the other 2 parents in the chat 'Unfortunately it doesn't work for us. How about you, can you take it on?'

People seem very willing to volunteer other people's time and money.

Put the chat on mute and ignore any comments for a few days.

I think the 'village' would tell a rude, ill mannered child that if they don't buck up their ideas they will be walking home. It's funny how the 'village' is supposed to be there to do things for children but not teach or remind them of their social responsibilities.

Google Narcissists and flying monkeys, it's a common tactic.

I think you have to be direct - I wouldn’t call it rude.

You could say - I do have to do my shopping and I’m not prepared to take your child with me. I am trying to be polite but it does not work for me for several reasons- which are private - to take your child.

You shouldn’t have to tell them your child’s diagnosis in order to justify yourself or get into an argument with anyone.

You could go the whole hog and say that the child was badly behaved but tbh you shouldn’t have to!

Takes a village my arse. Why doesn’t she offer turns if that’s the case. Or one of these other parents go out of their way and take him!l?

That was a massive assumption of yours to take parental responsibility without any previous discussion with parents. I wouldn’t have done it OP, unless it was an emergency situation.
The child was in the care of the teacher until handed over safely to the agreed person collecting. You had no such agreement and there was emergency so you actually placed yourself in a precarious position.
I know it’s sad to have to think that way, but this parent is untrustworthy, unreliable as well as cheeky, so please get out of this situation before it goes any further.
You need to let it be known to the teacher and parent, before the next session that you are not be taking responsibility for the child again and are unable to give lifts. You are under no obligation to explain why.

Tell them they can take the child home then and see them backtrack.

I think you are going to have to be blunt and just say that you were not asked and anyway if you had of been asked you were not able to commit so they therefore need to make other arrangements or call on the so called village.

I’d reply privately to say that you were not asked nicely to do this- it was assumed and the child’s behaviour on the journey was unacceptable.
i do think you should say no, but I do wonder why the other parents are so keen to make you do it? Is there some abuse or something you are unaware of?

Or 'I may have been happy to provide a lift again, however x child was incredibly badly behaved last week and injured my child, hence no more lifts.'

Stop making things up. Did you not even bother to read the full OP?

Last week she just left the child at the activity and told the child I would be giving them a ride home

How on earth you've managed to twist that into 'without permission' is beyond me.

Stand firm, an abrupt 'sorry that doesn't work for me' will put an end to it

Your mistake was that you :
1- put it in a group chat so invited all parents to discuss the issue
2- gave the reason so invited other mum to do suggestions.
you should have messaged the other mum privately that you have other plans and can’t give her child lift from the activity. Then notify the group leader privately about the situation, and then smile to the child if questioned and say : No, no Lauren, you are mistaken. You are not coming with us

Exactly this

Stupidly, I hadn't twigged that this was addressed through some "group chat" and never understand why these things can't just be sorted privately, without the need to invite others to pitch in

This was an obvious response from the CF. You made a rookie mistake - thinking a CF will be reasonable. Recovering this is harder than just a hard no to start.

yoy need to be assertive and say you have other commitments and can’t take little cow her kid

@DreamingOfHotPotatoes how did the child get to the activity last week? does the cf expect you to collect her today? do not turn up for her. let the cf figure it out!

Your mistake was that you :
1- put it in a group chat so invited all parents to discuss the issue
2- gave the reason so invited other mum to do suggestions.
you should have messaged the other mum privately that you have other plans and can’t give her child lift from the activity. Then notify the group leader privately about the situation, and then smile to the child if questioned and say : No, no Lauren, you are mistaken. You are not coming with us.

Now I would answer the village comment in the group chat: Yeah , the village would be very handy…. 🙂.
And then I would tag the other mum with her comment about shopping and answer her that you can’t unfortunately so can’t give Lauren lift back home. And then I leave it at that.
and on the day I would tell Lauren : no, you are mistaken , you are not coming with us.

Your OP reads as if she's expecting you to take her as well. That's easy, you don't pick her up.

I'm afraid I'd have no truck with this nonsense and send one more clear message that you will be giving no further lifts and that you were concerned that she didn't ask you personally last time and left it to her child.

Also let the group leader know what's happening.

I would guess the CF parent has been expecting other people to give this child a lift every week and they're glad to offload the chore on to you. I would make it clear 1. CF parent didn't have the courtesy to ask you and 2. the child was rude and badly behaved. So it's a no from you.

Just say - “sorry, this doesn’t work for my family”. Repeatedly

and just ignore other parents “questioning” you, no response to their messages
if they confront you in person, then repeat the phase above

You don't need to be rude at all - simply tell her this doesn't work for you, ignore completely anyone else who tries to chip in, and if she's unpleasant enough to ask why it doesn't work simply reply that you don't want to do it

The "village" comments. Astonishing.

I can't decide whether I would completely ignore or make a barbed response like those suggested above.

I think on balance I would say nothing. If anyone from the group asks you about it in person I would refer to (in this order): distressed autistic child; badly behaved child shoving and kicking your child and you; concern that no parent at home when child returned (safeguarding) and rudeness of parent not asking, thanking or proposing reciprocity which you find intolerable. If they don't accept that they can shove their "village" where the sun doesn't shine.

OP said that this child pushed her child out of the way and demanded the front seat. I'm assuming that OP said no and put her own child in front, following which the other child kicked OP's seat the whole of the way home as they were angry about not being allowed in the front.

Excellent so, that means one of the other villagers wont mind getting off their arses to do it from now on. I have had it with CF's recently myself and at this point I would just be as rude as they seem to be.

I would simply reply 'I'm sorry but for perdonal reasons this doesn't work for me and my child. Best wishes'.