Cleaner

she didn't want to do the other job.
nor did she want to say so bluntly to you.
both you and daughter should have realised that by now.
actions speak louder than words.
just carry on as you are.
or if you prefer to be proud about it, get rid of her.
and try to find another one.

If she's good keep her and don't mention your daughter again. I wouldn't go so far as to say she should do her own cleaning without knowing her circumstances only you and she know that. If one is needed, see if there is an agency in her area. You might get a shock at what they charge. One by word of mouth is usually cheaper.

Has she let you down? If not, then your daughter can make her own decisions. If yes, then you can make your decision.

Keep her is

Keep her, good cleaners are difficult to find.

There’s an old saying “ Don’t cut your nose to spite your face”.

Good cleaners that you can trust in your home are few and far between. You obviously think she’s good or you wouldn’t have suggested her to your daughter. Keep hero’s my advice unless you already have a replacement lined up.

Absolutely keep her! I have had shoddy cleaners and star ones. The latter are hard to find! My current cleaner ironically also let my daughter down with a poor job at the the time of her move, have I let her go? No!

Pedants' corner?

I would keep her if she does a good job. She ought to have told you she was too busy/ didn’t want any more work/ too far to travel to daughter’s/ whatever, but probably thought you would be offended or something, and chickened out.

No point in both of you having to find a new one is there?

I am with Hetty all of the way.

Really good cleaners are hard to find. IF she is really good, keep her.

Keep her; you don't want to lose a good cleaner and there may be reasons she doesn't want to work for your daughter.

I'd keep her. A bird in the Hand etc etc

I’d keep her, she hasn’t actually done anything wrong. Some people agree to things just to be pleasant, especially some Asian people so perhaps it was something like this.

I wonder if your housekeeper is too embarrassed to tell you she is too busy for fear of offending you? Or perhaps your daughter's domestic set up will be more challenging than she can take on at the moment?

I'm with Hetty 58 - let it drop and your daughter can do her own running round. Or her own cleaning. Great exercise, free, saves a trip the gym etc. etc. etc.

I can't see the point in losing a good cleaner. I'd just accept that she made some mistakes with her 'promises'. Don't 'cut off your nose to spite your face'!