Hi there, we've had two 'nannies with own child'.. both had their babies at the start though, and both went on mat leave and did not return.
I didn't pay less for Nanny with own child, but with hindsight, (and were I to have a nanny with own child again), I would.
I now have a nanny without a child, and the difference in what my children are able to do / plans for trips / order the house is in etc. is very noticeable in my case. Having said that, both my NWOC were lovely, totally reliable and very high standard, and there were definitely plus points, but my current nanny and her child-free status would be my future preference.
I think it's right to renegotiate, especially as your nanny said she wasn't planning on bringing her baby in the first instance (although you were obv right to second guess that!).
The 20% reduction sounds very fair to me. Tough as it seems, if your nanny isn't happy with that (which she may not be, and I can see both sides as she may initially think she can carry on as exactly as before) I would consider if you are better off with a new nanny.. Very much depends on how you value your nanny and what her bond with your children is I guess.