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

Just say "I'm afraid I won't be able to drop darling Cecilia as this is inconvenientfor us" no further explanation required.

Just tell her in advance you’ve got commitments in the opposite direction immediately before and after so it’s not practical to drive her any more.

This is perfect--OP do you feel comfortable trying this?

You don't owe this woman any explanation
Don't lie or make up reasons it's none of her business just a firm no
Tell her you've informed the coach of your decision so not to involve him/her by putting pressure on them. I spent many years ferrying my kids to various activities and that me time to discuss the day was precious and comforting especially if your daughter is struggling with peer group dynamics

This is an opportunity to set an example for your daughter to stop rolling over for bullies and accepting one-way relationships with "frenemies" who just use you when its convenient for them.

Do your best to take all the resentment & anger out of it. Tomorrow evening, text the mother "Hi [mother], I wanted to let you know in advance that we will no longer be able to give [daughter] a ride to or from [activity] on Thursdays. I'll be letting [coach] know today as well so there's no confusion. Have a good week." Then tell the coach (and cc any relavant office people) the same.

If she asks, or if the coach asks, be matter-of-fact about it. "No, as I told [mother], we won't be able to do that anymore." If they press, act a little taken aback "Surely [mother] wasn't relying on me after I so clearly said I would not be doing that. How strange. But as I said..."

Just say no!

Once you start saying no to people and being known as hard to deal with it comes quite easily and people stop taking the piss.

Just make sure your car has no room to pick her child up. Carry some empty/lightweight cardboard boxes on the other seats "to help out another friend" and suggest you have to do this every week and cannot change that schedule that requires you so this for your friend. No need for extra details. Tough shit for the other girls mom but she created the situation.

You both sound equally dreadful! Frenemies? A child says that or did you as an adult?

This.

This girl told me she doesn't even like going, she says it's boring but her mum says it'll look good in a university application! They've not even sat GCSE!

Unless she's planning on uni in the US, or doing sports science, it will have no relevance whatsoever.

"No, I can't."

"No, it's not convenient".

Or if you want to offer a sop, say,

"Sorry, I can't do that. I can take her to my house and you can pick her up there."

If she has to do the four mile detour she may suddenly find she can pick her child up from the club.

Tell her you have to do something on the way that means you can't collect her child and bring them back etc or get a motorbike and you are laughing. I'd just send a text. "Hi CF I'm afraid this week I'll not be able to take CFDD to sports as we have to call at DD's aunt's on the way back and I have some errands to do on the way there. It may be tight next week too as we are hoping to make Aunt's visit a regular thing as it's on way home and could be home late. May be best for you to organise some alternative transport hereonin. Thanks

Hell NO!
Why would she offer to take the child to her own house. That's even worse, she would end up feeding her on top of the mum being a cheeky fucker.

Sooty but I’m going to rant as this is yet another post where I just want to shout

Get a grip and grow a spine!

You don’t have to do anything you don’t want especially if it puts you out

What do you think the advice on here is going to do that you can’t figure out for yourself?

This isn’t asking about various choices - you either carry on which you don’t want to do - most would agree with you. So in that case you need to pull up your big girl pants and tell her no! It’s not that difficult

No thanks, the kids aren't friends, we aren't friends, not my problem.

Absolutely this, in fact I wouldn't even bother with the "Sorry".

You simple say no! Or write out a message to both coach and mother that you will not be taking her home any more. Regardless of any circumstances, she needs to prepare better for when she can't make it to lift her daughter.

I had something like this happen to me and I knew I would be seen as the 'bad guy's but I genuinely could not give a shit. Why do we always have to sacrifice our peace for people like this?!.. you are not responsible for her daughter... She is.. an her behavior is a bloody disgrace...!!!

......now I have to drive 4 miles out my way to drop them back.

No. No you don't.

Learn the sentence 'Sorry, that doesn't work for me' and repeat it as many times as possible.

Is there any scope for changing time/day and then just tell her DD has stopped going?

Haven't RTFT but your replies sound like you're appeasing the other mum because you're a bit scared to say no. If you can't stand up for yourself, can you do it for your daughter, maybe seeing you say no would help her stand up for herself too.

You're not abandoning a child by refusing to take her, surely she's the coach's responsibility while her parent isn't there. How old are they, you talk about GCSEs so they must be teens.

Mumsnet mantras apply here, ideal scenario "no is a complete sentence" if you don't take her, and her CF mum doesn't turn up, the coach will have to resolve the problem.

If you don't feel able to do this, weaponised incompetence is next on the list. "Hi CF mum, I told you I couldn't drop spoilt brat home tonight so she's at our house drinking sugary caffienated drinks, eating brightly coloured sweets and any other vastly inappropriate things I can think of. Please collect ASAP. We're walking the dog in half an hour, so she might be a bit muddy if you can't get here before then"

Also to add it would be the coach waiting with the friends daughter not you, if the coach asks you explain no arrangements were made and you have to leave right after and go somewhere. Trust me the coach will not allow it to happen again

Agree with this, after a few weeks she will hopefully get the message and stop asking especially if it becomes part of your new routine. Id probably use the check in with a relative who lives nearby, you could be sorting their dinner and need to call to the shop before the activity.
Id love to just say no but would find it awkward.

Well you are saying your child is a doormat with the other child but that's what you've taught her! Put other people first and don't stand up for yourself.
I've demonstrated the opposite with my dd and she certainly stands up for herself.
Stop being such a wet blanket!

I'd concentrate on teaching my daughter about self preservation, standing up for myself and not being taken for a mug.

next time coach says you have to take madam home, say no. Come on.

I would just tell the other mum that you'd like to spend the drive time with your daughter as it's meaningful to you because you work too and are limited on time and you want to be able to speak to her about her day and how she's feeling about school etc now shes growing and hormones etc. Or something on the lines of this. I find talks in the car more freeing and open with kids.

Why did you say yes? I haven’t gone through all of the comments but if it was me, I would come up with an excuse and not do it.