Have you been giving annual pay rises, or has salary been fairly stagnant for several years? Whilst you may view 9.30-11.30 to be time when the nanny should be unpaid, if you have not given pay rises for a while then you could view some of it as being a pay rise, though it isn't as the nanny gets no extra pay, gets some non-contact time instead.
Non-contact time - that's a useful way of looking at it, as unless you are in a job where you can drop things at a moments notice and pick your child up from school, the nanny is "on call" for anything that may occur.
She has been clear she will do kids' laundry but not ironing or cleaning for us which is fair enough.
Surprised she is not already doing some of that. Kids laundry does pile up and there is bedding as well to be done. General tidy around, not the same as deep cleaning the bathroom, is surely reasonable to expect if you are to continue paying usual salary for non-contact time.
Has anyone successfully changed their nanny's hours, or are there any creative compromises I'm not thinking of?
My hours have varied quite a bit over the past 5 years and do vary on a week to week basis sometimes due to my employers needs. However I still get paid for a specified number of hours per week, regardless of if I physically work those hours, or if they are contact or non-contact time.
will I find someone who would accept having two hours unpaid between 9.30 and 11.30am
Unlikely as they will still be on-call, will not be able to take on other work for such a short period, will be needed those hours during school holidays.
If you changed to using a childminder, many would still charge you for time a child is at pre-school. It is not until the child is at full-time school that costs change. Have you given thought to what will happen in a few years, when all your children at at school - are before/after school clubs an option in your area and would they fit with your timings?
What start time and finish time does your nanny typically have? That may be a key factor as you may not find any other form of a care for those hours. Could you change your work pattern such that you could take your child to pre-school? Then been near ish so you can be on-call. Then have a nanny for say 11.30-7pm? (or whatever time) Finding someone to do those hours may be easier than finding someone to come to your home, do a couple of hours, go back home, then come back to you again and do more hours. It's the travelling back and forth that adds to the employees costs and thus someone doing that may want more salary for the hours they are working.
Im sure she wont want to reduce her income by much.
Have you actually told her about the situation, asked her if she would consider having unpaid time during the day? Do not make assumptions as you do not know someone's financial situation - they may have needed the income when they started the job but things change over time and they may now be willing to renegotiate the salary. Easier for you and for them if they stay in the job - no job hunting for example.
So it comes back to that pay rise question - if they have not had a rise for a while, then they may be willing to renegotiate the salary so that they are paid more for the contact hours and paid a 'on-call' rate for the non-contact time. However the cost to you may well be very similar to now, so not a money saving.
Pre-school is optional and you certainly do not need to send a child 5 mornings a week - they may well benefit from a day or two at home, doing things out and about, visiting friends, having friends over to play.