Of course it is fair to ask the nanny to take a paycut. I can't believe that anyone thinks it would be unreasonable.
When thinking about how much, I think it depends on whether you want a nanny-share arrangement or a NWOC arrangement.
In a nanny-share things must be split equally. The nanny's child would be of equal importance to your children. If the nanny wanted to do something with her baby or take her baby to a doctor's appointment, for example, you will have to accept your children going as well, in the same way the nanny would have to take her child to an activity your children want to do. I think you would have to expect a reduction in other jobs e.g. laundry etc as well. In this case I would reduce her wage by 33%. It's a share, you have two children 66%, she has one so she pays 33%.
In a NWOC arrangement, the nanny would put your children first and her baby would just 'come along'. She wouldn't be able to dictate what activities she wants her baby to do, she would carry on with your children's routines, activities etc, her child just fits in. She would be expected to do the same job as before. In this case I would reduce it by 10-15%.
All the nannies I know who bring their DC to work have a NWOC set-up i.e. their child fits in with the other child's needs.