OP, we did this with our nanny of 3+ years last year. It was hard, but necessary. Here is what we did:
- planned to be very generous financially (as you are)
- picked a time when husband and i could do it together, on a friday afternoon, and when we made arrangements for the kids to be elsewhere
- had a letter for her, outlining the severance we were giving, our thanks for all she had done for our family, and our plan for the next few weeks.
- stated in the letter that we hoped she would work through April 30, and on her final day we would hand her a wonderful reference letter and the final severance check of X.
- We also stated that we would be happy to help her look for her next position if she wanted our assistance.
- We were brief in our reasons for making the change, and we were not specific about negatives. We wanted to take the high road as we certainly didn't wish her ill, she just wasn't the best fit for us any more (nor were we for her).
As soon as we told her we let her leave. She was upset, there were a couple of difficult minutes, but we had prepared ourselves to just have a few basic statements and not get drawn into bickering or anger or emotion. Our basic position was "Thank you so much. You have been wonderful to our children and us for the past three years. We will always be grateful for everything you have done for our family. As our kids are older now we need a change for them, and a different solution, so we are ending your employment. Here is what we are doing to thank you for time with us, and help ease this transition..."
As we planned to have her continue working for a couple of weeks we didn't tell the kids anything, but we were prepared to handle it if she chose not to return (which didn't happen.) We made the final severance payout, and glowing reference letter, conditional upon her continuing to do her job for the remaining period, and on her not discussing her departure with the children other than in the way we outlined.
We told the kids that she was leaving to go help another family take care of their baby - that they were bigger kids now and she was needed for other babies. We didn't tell them any of this until we had gotten through the first week, so we could be comfortable feeling that we could all part on decent terms. Once we could, we were able to say that they would still see their nanny regularly.
It took our nanny almost a week of work to be able to think about her next position, about starting a search, to not tear up at the end of every day, to make eye contact with me, etc... And when she left it was hard.
But a year later she stops by and visits, has babysat for us twice, came to the kids' b'day party, and sometimes just pops in to say a quick hi when she's in the neighborhood. We helped her find her next job (which offered her an infant again - her true passion, among other things she wanted) so she is ok. And the kids adjusted to their new nanny pretty well also.
I posted here quite a bit around that time, seeking advice and offering updates, so you might find some of those threads if you dig a bit (especially in the employer thread).
It will be hard but just keep your eye on the long term goal and what is best for your family. Financial generosity definitely can ease things, as can the promise of a good reference.
Good luck.