To be expected to run around after another's child?

You’re not abandoning the child, her mother is. You have a very important appointment to get to immediately after the class so you are unable to take the child. That’s it. This isn’t your problem and she can’t make it yours if you refuse to get involved. Every week she asks just reply back that you’re sorry but you’re not going home as you have an appointment so you can’t collect/wait with the child. Tell her not to worry, you’ll let the coach (who’s paid to be the responsible adult here) know that she can’t make it again so that they can ensure the dc isn’t left alone. Make sure it becomes coach’s problem because they will not tolerate this and I doubt she will pull this shit again.

"I obviously can't abandon a child there."

You are not abandoning the child - she is

Get it done - the first time the coach is stuck with the kid will be the absolute end of it though and possibly the end of frenemy attending the activity at all, with any luck, as they absolutely will not tolerate CF mum doing this to them!

I wouldn't faff about being nice either.

To CF Mum: 'I've neither the time nor the inclination to run around after you/your child. No further lifts will be given, do not ask.

To Coach: Frenemys Mum is a CF, I won't be taking Frenemy home, it is not on my way even remotely. Heads up you're going to be expected to wait/run kid home!

Yabu not telling her to f/o. Why would you facilitate her child trying to pip yours at the post out of spite from the mother? Easy way to resolve this issue is to say no, I can't facilitate xyz until either she does it herself or the kid drops out. Your child and their happiness comes first.

Just not turning up and hoping someone will ferry their kid around so unbelievably cheeky. You have absolutely no responsibility to that child. "No I can't" to both the mum and the coach.
I wonder what other inconvenience of parenting she off loads on the overly polite!

All of this. Put your daughter first.

Of course you can ignore. Don't answer. Gather your child up and go home. If the coach comes over to say 'Gemma's mum has asked if you can run her home,' you reply, 'Sorry, I can't. I have somewhere I need to be and it isn't on my way'.

It's not rocket science. It's not your responsibility. Leave them with the coach. They will contact parents presumably.

I'd message her saying something like, "Hi, just letting you know we can't give x lifts to or from coaching from now on."

Then ignore any whining and decline any requests passed on by the coach. The parents won't abandon their DD but they will be forced to take responsibility for her.

Actually it is nice. Op needs to respect herself, the other woman certainly isn't.

Just say no.
No context, no further discussion, just no.

Why are so many people scared to use such a simple word these days?

Totally agree with this, be an adult and just....say no? You get a call or text..... just say no, they can't collect their own child from a club they knew she was going to......that's their tough shit. The child is not your responsibility, set an example to your own DD that it's not acceptable for people to take the piss.

You have nothing to feel guilty about so say whatever you like, depending on what works and lie if you want to. I’m sorry I can’t tonight because….
we’re going via the supermarket/picking up a takeaway/popping in on a relative/need to go straight home as husband’s forgotten his key/life is too busy to be able to do this each week.
Don’t answer your phone and if coach asks just say sorry we aren’t going straight home so can’t do it.

YABU to be doing the collecting etc. you say no that doesn't work for me.

Honestly why did you say yes ?

@WoolyMammoth55 has worded this perfectly, @Blondeandbeautifullol!

Make it the coach's problem: sorry no we can't.

The entitlement is breathtaking! You need to put a stop to this by telling her and the coach that you can no longer bring her home as it’s too far out of your way-and to please not ask again.

YABU, the word No can be so liberating. Try it, what's the harm? Once you do you'll find it easier and easier to say it.

Just say, sorry that's not going to work for us. Stone wall. Or grey rock or whatever it is.

The effrontery of this woman is genuinely astonishing.

I completely agree with PPs - tell her that going forward you will NOT under ANY circumstances be accommodating her requests and update the coach too.

I suspect she will push back in some way but no matter what do not relent. Draw a clear line in the sand. If that means her child is left with the coach and no ride home - so be it.

She's almost certainly not telling the truth about being unable to collect her DD, she just wants you to do it because you're already there.
Just say to the coach that it's not convenient, CF Mum will have to find someone else to collect her DD. Don't respond to her phoning or texting you.
Also the whole debacle about training and teams is very weird.

Well obviously you tell the coach that you are not able to offer a lift to this child under these circumstances, and if they ask why, tell them why. That this woman is expecting you to be her taxi driver, she is taking the piss, and you won't do it any more.

In an emergency, and if you are there, you could bring the child back to your house, and the woman can collect her dc from yours, but every week? No.

Stuff that for a game of soldiers.

This. The coach probably thinks you’re fine with it. Tell them both you’re not.

"I totally agree with the just say no replies. However, this is the first time I've been asked up front. On 4 prior occasions I've just been called or messaged during the sports class directly, or when i ignored it via the coach there that she's unable to collect her daughter now so can I bring them home. I obviously can't abandon a child there. But it's every week!"

Hi OP, I do understand that you've been taken by surprise previously and felt on the spot so you couldn't say no.

Right now, the thing to do is to send a text message to the CF mum saying: "I have been hugely inconvenienced a couple of times now by you asking me to drop your child home at short notice. I won't be able to do this again and wanted you to know this now so that you won't ask again. Please ensure that there's some alternative emergency provision in place. If I'm put in the position of being asked again I'll have no choice but to say no, and that might distress your child. Thank you."

And for good measure send a similar one to the coach, saying: "I have been hugely inconvenienced a couple of times now by CF mum asking me, via message to you, to drop her child at short notice. I won't be able to do this again and wanted you to know this now so that you won't ask me again. I really don't want to be put in an awkward situation again, please. I have messaged CF mum directly to advise her of this. Thank you."

CF mum might reply protesting but if you ignore her then there's nothing she can do. Best of luck!

Just say no it does not suit me and nothing else every single time. It’s not rocket science. Do jot be a doormat. Why are her wished trumping your own?

What's upset me is every Thursday, I now get messages to drop/collect/wait with her child as this Thursday evening club is not convenient for them.

Ignore the messages. Reply later that day and say no, sorry-that doesn’t work for me.

You aren’t her chauffeur.