I've seen several posts asking similar questions on this forum, and I don't know that I've ever seen someone chime in and say that it works for them, nor have I seen an op come back and say that they were able to figure it out. In the end it just becomes too difficult to financially please all 3 parties.
For instance if I were your nanny, I would expect slightly more for caring for 2 kids in a share than I currently do for caring for just your two kids (to account for the difficulties of dealing with two families and their different needs, philosophies,etc). Given your current rate, I would expect at least $25/hr for the share, and that's probably a low end rate.
That's simple enough, the real difficulty comes in with the extra child. As a nanny I'd expect to make more for those hours, probably around $30+. But as the other family I'd expect to pay less for these hours as my child would get significantly less 1:1 attention. So if I was paying $12.50/hr in the above $25/hr two child rate, I might expect to pay around $10/hr when the third child is added in. This leaves you paying $20/hr for your two kids, which is only $2/hr less than you were paying without all the hassle for a share.
You might decide that with the overall savings while your older child is in school that it's still worth it, which is fine. But I think a lot or parents end up realising that with school holidays and sick days and snow days, that the savings just don't justify the hassle.