A nanny share can absolutely work but you need to be very clear and upfront from the start on expectations and what happens in situation a vs situation b.
I would also, personally, highly recommend that it is NOT always at your house. You become the default "person in charge" - the nanny sees you as the primary parent, you start to feel you can control everything, the other parent might get resentful and it gets complicated with food, toys use, damage/wear and tear etc. Sharing it is a much better idea.
You should also agree upfront very clearly under what conditions the relationship would end, and how that would work ito notice periods etc.
A few things to consider, for example:
Food - who pays, who decides what to eat (and when), how is the shopping and meal planning organised (another reason to take turns re houses as then whoever's house it is organises/pays for food that week).
What are the expectations for the nanny in terms of days out/ how far to travel/ how to travel. Are you aligned on her meeting up with nanny friends / when she should be checking in with you on plans / types of activity. (this may seem like a small thing but is actually fundemental. Some parents want nannies to go no further than x distance, preferably on foot, others want pre-discussion on every activity etc). Ditto, what costs are you both willing to meet for these days out/activities and are you aligned?
If one child causes damage - a spillage, a broken toy, a damaged car seat etc - and it's in the other child's parents' house/item, what is the agreement about any mitigation?
What happens when the nanny is sick or on leave? Will you each take your own child or agree a system whereby one family has both children? Similarly, what happens when one child is sick? A dedicated nanny would be expected to look after a sick child, but what about the other child?
Similarly, how is leave decided and agreed on? Most nannies have an agreement that the family decides two weeks and the nanny 2 weeks. How will you, as families, negotiate your two weeks?
These are just a few examples.
We did one mini-nanny share (ie we shared the nanny on certain days, but not full time) and we talked about another one. The second one didn't happen because the other person, it turned out, very much saw it as HER doing US a favour by allowing us to "share" her nanny. So we backed quickly out of that potential arrangement.