When we did a nanny share we split the cost according to how many days childcare we got from the nanny. She was with me FT and the other mum worked 3 days, so I paid 5/8 and she paid 3/8. We did the kitty this way too, for food and activities.
Babies both at my house which suited us all. If you split houses you need extra cots, high chairs etc at both houses.
Remember holidays - you all need to take holidays at the same time, unless the parents get a lot more holiday than the nanny. Nanny picked 2 weeks, we picked one week each.
And what will you do when the other child is sick? Just get chickenpox too, or will the parent of the sick child take time off? This is the biggie, for me. One of the great advantages of a nanny is that you still get childcare when your child is sick.
That should get you started....
Don't think it's all problems! My DS1 is still astonishingly close to the child he shared a nanny with, even though the share only lasted for a year, and ended about 6 years ago. We've moved away, and see the other family about once a year now, but the boys greet each other like long lost friends every time.