to ask friend if she is going to pay my teen for cat sitting

I think you need to text before you see her on Friday. Especially if you were planning on waiting to see if she brings money. So you get there, you wait for her to produce payment, all the while dreading the discussion and awkwardly waiting for the right moment.
You need to be breezy but firm as if it was assumed she would pay eg
’I’ve just realised I don’t think I gave you DC bank details for you to pay him for the cat sitting’. This way, she’ll either reply agreeing with you and to you sending his details, or she’ll be forced into admitting she wasn’t going to pay him or thought he was doing it as a favour, which will be embarrassing for her as who expects 10 days of cat sitting to be free? And you’ll be able to respond ‘why did you think he’d do it for nothing?’.

This!
but for £15 a day, as that is the precedence you have set with her daughter and the hamsters.

You need to be direct and assertive otherwise your awkwardness is actually letting your daughter down, and setting a terrible example for her to be taken advantage of.

Message your friend that you are teaching your DD how to handle personal finances, then get DD to send an invoice over!

If you are meeting I would text ahead and say also just wondering if you needed DD’s bank details or if you are giving me the cash tomorrow. DD can’t wait to buy X on Saturday, she’s been saving up for a while now.

Way too little! 😁... This will teach yer daughter to be significantly put out... It's 20 visits for a pound a time?!

Unless you have some how previously indicated to her your teen is absolutely cat mad and likes nothing more than spending time with cats - why else would she 'want' to feed her cat twice a day unless it was for money. She asked if she wanted to - not would she do her a favour.
My friend's son /son's friend came and took my dog out for a walk when we needed someone and we were all working that day. I offered to pay him as it was a one off - he said no as we had taken him on holiday with us. I offered to pay his bus fares and he had a pass - but even as a one off I wouldn't expect a teen to want to do it for free,

Could you message her with your DD's bank details? In a nice way, something like 'DD says cash is for old people like us now, here's her bank etc."

If you are meeting her on Friday I would text her on Friday with the hint mentioned above. Less awkward than having to raise it face to face and if she had every intention of paying no harm done.
This one experience will stand both you and DD in good stead for further casual employment opportunities while she is studying ...like babysitting for instance. Some people are very generous but some people take terrible advantage. From now on she will always discuss payment up front. A good life lesson learnt 💐

To be honest I think you should have discussed it beforehand! You can't ask for money now!

It should have been like this:
friend: Hi will X cat sit for our cats?
you: oh yes sure, when are you away?
friend: monday to thursday
you: yeah that's fine, how about £50

etc

£15 per visit - Thats a good rate

Yes this is exactly what I would do. No hinting or asking, just a bright and breezy expectation of payment and does she want teen's bank details or will she be bringing the cash on Friday.

She would have to have the brassiest of all brass necks to not pay after that. A text avoids the face to face awkwardness (though she is the one who should feel awkward not you) and gives her a comfortable way of saying "oh yes I was just about to ask you" or "yep no worries I have planned to stop by the cash point before we meet".

If she asks for pet sitting again, agree the sum or rate up front. If she is scatter brained as you say, rather than a CF, she should be fine with that.

She's not a good friend if she treats you and your daughter like mugs. If she doesn't offer the money I would hope you'd discontinue the friendship and tell her why.

Quite apart from anything else, what kind of CF lets ANYONE, even a ‘good friend’, feed their cat twice a day, having to drive a significant distance there and back, for 10 days, and not immediately offer them ANY kind of token of thanks, even a petrol-station box of chocs? I’d be ashamed of myself for being so ungrateful.

I don’t think this is as good a friend as OP thinks and I’d also be inclined to think that zero recompense was being contemplated for DD’s services, I’m afraid.

Speak face to face op.on Friday it's much better than texting.

she's trying to get away with getting it for free

I know you feel a bit awkward but you need to be assertive on your daughter’s behalf. Just ask her when she intends to pay DD.
And if you and DD pet sit again, ask upfront how much she’s paying! Good luck.

DD has done pet sitting for years and money is always agreed up front
Maybe your friend forgot or maybe she is a CF, either way keep asking for the money

If the cat owner had had to go away suddenly because of a family crisis/ sudden death/ funeral then maybe the OP could be understanding and flexible and view it as a favour to a friend. But the cat owner went away on holiday and I am pretty certain the hotel/ air B and B owner/ booking agent all expected payment, in advance. Paying for cat sitting is part of the expense of going away as the cat owner well knows because she has paid for it before. Giving her a freebie is simply not an option or fair to the OPs daughter.

The time to ask was before the cat sitting started. Especially when you've done it free in the past. Your friend is mean though. I wouldn't bother with her in future.

Just send a text saying do you want me to get teenager to send her bank details for cat sitting payment transfer or does she want to bring cash to the coffee meet up tomorrow. That way it definitely implys she’s expecting payment and you don’t have to stress asking over coffee. Be bold. You are in the right.

I would message beforehand and say something like

hi friend, I’m looking forward to seeing you Friday! Is it easier for you to give the pet sitting money for dd on Friday or would you rather bank transfer her? I’ll send the details if bank transfer easier. Can’t wait to hear all about your holiday! See you soon x

Good idea to send a cheery text TODAY asking how she'd like to pay. Much easier than leaving it until tomorrow - if she hasn't got the cash on her, or dodges the issue but you've left it until the end of your meet, you're no further forward and it'll be even more awkward.

Always ask first regards to payment, with no mention about money, she more than likely will not pay.

In the nicest possible way, you need to sort this out properly for your DD sake, it’s not fair to keep her hanging because you feel awkward and are dithering about it. It’s not DD’s fault that you didn’t confirm payment before agreeing to this. Take a deep breath and text your friend today, or if you are too scared to ask then just give your DD the cash instead.