Who is in the right here, work wise?

speak up next time op
you were happy to start later but you needed to leave at 12.30

didnt you have a clue she would want the 3 hours despite starting later?

she should have said she wanted your usual hours but starting later
you cant blame her for wanting to round it up, but as said above better communication needed

I would pay the full amount because of the short notice. It isn't fair to mess people around especially when the hourly rate isn't huge.

I disagree that it was a breakdown in communication. I think she was rude and comes across as quite entitled.

At around 12.25, she said she had to nip out and could I stay half and hour more.

This bit is key. She knew you were finsihing at 12.30 (plus you said you'd already told her that) and she didn't like it. So she asked you to stay half an hour more, minutes before she knew you were about to leave, and then was late back from that. Asking you to stay half an hour more means she knew you were leaving at 12.30.

Then when you went to leave, 12 minutes before the time she decided was acceptable to her, she was miffed and yes she was rude to you.

I would say that she wanted you to stay until 1.30 and then made damn sure that you did, regardless of the fact she knew that wasn't the agreement.

Aside from any of that, she was rude to you. You adjusted to accommodate her change in start time and she took the piss. Next time she asks for a change in time, say no. Even if you can do it. I think she is possibly taking advantage of your good and flexible nature and may do her some good to be told, nope can't do it this time, sorry.

She was presumptuous and you lacked assertiveness.

Learn the lesson from this and do not be so agreeable in future, you have to learn to say no. I have had the same experience in the past. When trying to help people out, they come to EXPECT you to always agree. This is wrong on their part.

You have to learn to say no, sorry I have plans, even if you don't sometimes. Especially at last-minute requests. This means they are less likely to take advantage of your kind nature and assume you will always help them, with no thought about your own plans.

Do you have your work hours in writing? If not, I would just clarify EVERY time they change or tweak your hours, text message confirmation. Something like 'Just to confirm the change of work hours for tomorrow: 10:30-12:30, 8:30-1230 ' etc. Always keep the work our end time the same, unless they specify they expect a later finish. This should be confirmed at the time of them requesting the later or earlier start. If they don't mention it, you need to state I still have to finish at 12:30.

Can you speak to her and say that. Flexibility is only good if it works both ways. If it’s not working for you you need to say.

I’d chalk it up to misunderstanding. I think she wanted you to work until 1.30. So just start later but still do 3 hours. She should have been explicit.
In future I’d just be clear. Yes I can do 10.30 start but I need to leave at 12.30 as usual etc.

I agree that it was probably a misunderstanding, she thought you were still going to do the 3h.
Our cleaner had similar issues with some of her customers who kept changing the times with short notice. She introduced a new condition to her contract that any changes needs a week notice, or the full amount is due for the contracted hours (so in you case she would have come at 10:30, worked 2h and be paid for the 3h).
I think it's fair!

Well, as you only usually charge for the two hours when they ask you to start kate, I'd say swbu in expecting you to do the full 3, and was quite rude in her coercion. I wouldn't particularly want to work for her after that, but if you do then just mention miscommunication, tell her you had had things you'd needed to do so you need to clarify for the future. Make sure she knows that you do only charge for the hours you actually do, as she may not even have noticed that and assumed you're just taking a paid hour off each time.

OP said she only expected too be paid for 2 hours

If you are employed for 3 hours, then yes - I would have expected you to work 10:30 - 13:30. However, as an employer, I would also make sure I clarified that with you, especially if I am asking you a favour.

Just make sure you know next time - you don't want your employer thinking you are taking the piss.

She clearly thought you were being rude, just like you think she was being rude. Misunderstanding all round.

Maybe she thought you were rude, but so what? Her attitude sounds pretty entitled

If you said “I normally work 9.30 to 12.30 but today I’m starting at 10.30” I would assume you were working 10.30 to 1.30. Anything else is a bit cheeky, you’re expecting to be paid for an hour you didn’t work?

That's surely the only explanation for her curtly pointing out the time to you as you were leaving. I think she's in the wrong. If she expected you to stay for three hours but with a later start time, she needed to have explained that, because you could have had stuff on after 12:30, planned your day, etc.

There's definitely a communication issue here. In my opinion, it is up to your boss to explain exactly what she means and be clear but I guess if she doesn't, you can and should clarify and there are obviously slight shifts according to to what you do for them and the history/set up etc.

eg, my cleaner asks if she can come a bit later, I assume she'll still be doing the same number of hours, just starting later. Ditto, if I ask her to change the slot, I'm asking for the entire slot to be changed. I think based on our interactions, we'd both understand that. If I asked her to change at the last minute, and she couldn't, I'd expect to get fewer hours but still pay for the full amount.

Couldn't have put it better!

You both need to improve communication.

Ask for clarity in future over when your start time is delayed, are you expected to work full hours, or reduce your hours. They shouldn't be constantly reducing yoru hours unless you're fine with that?

And secondly, if you are asked to stay to cover, is that paid, and if so is that full hours only?

That's definitely what I would do in future. That gives them the opportunity to change their mind about your start time

I'd have raised it with her at the time, that she said she'd be 30 mins, it's been 45 mins, I need to go. A bit of asserting yourself won't go amiss. But in the future I'd get clearing in texts because it seems they're a bit flakey.