I honestly can't much advantage to you for this situation.
In fact, the only advantage I can see is financial.
Putting aside all the pitfalls - location, nap schedules, activities - that must be compromised on. Can you even imagine a way to be fair financially to all the players? THe nanny needs a significant raise. You should get a significant discount. Is the new family going to be willing to pay enough to cover both of those things (since they also should be getting a discount off of private nanny care)
Also, are your kids heading to preschool any time soon? You can't lower your nanny's wage when that happens. But I'd certainly expect to shift more of the cost to the infant family when that happens. Is that ok with them?
Personally, I think 2:1 nannyshare splits are very difficult (not impossible, but difficult) to work out to be fair and worthwhile to all parties.