This is going to be long, but here goes...
As a former nanny, who did do shared care successfully, my first recommendation is to have *everything* in writing. Everything.
Here are some of the questions I've dealt with during this sort of arrangement:
1. What is the shared care hourly rate for the nanny vs the private hourly rate? (You will want to know this in advance.)
2. *Which* hours in the day will be shared vs private?
3. In the case of one family or the other having to cancel that day's care due to illness, how is the nanny paid? Will you pay the shared rate for care not used? or does the family utilizing care pay a private rate?
4. In the case of illness, does the nanny stay with the first family (milder illnesses) and provide care while excluding your child or does the nanny come to your house?
5. What are her provisions for health exclusions? (I chose not to do 'sick care' as I had several clients and couldn't afford to A. miss work and B. leave other clients in a bind.)
6. Do you have back up care for times when your child shouldn't be in care? (pink eye, bad cold, other contagious situations)
7. Insurance liability. I had families sign mutual waivers that each parent would cover their child's medical costs and verified they had insurance; any damage to property would be filed through homeowners insurance, and I privately took responsibility for any damage to my person or property (I wear glasses; had a child broken them I would be responsible for replacing them.) Deciding early on who is responsible for what eliminates a lot of arguments.
8. Food. Will you pay a stipend to the host family for them to supply food/snacks; will you bring a bunch of snacks/food to share, or pack your own child's food?
9. Naptimes. There should be adequate and safe accommodations for the children to sleep. Do you need to bring a pack and play for your son? A one year old will need containment and children should not share cribs.
10. Agreements regarding television/electronics etc. They might be fine with some cartoons or shows you feel you don't want your 1 year old watching. Something to think about and discuss.
11. Childproofing and baby safety: are there barriers to stairs and other hazards in the house? Families have many different philosophies on this.
12. Ask the nanny how she handles disagreements and squabbles between kids and how she deals with potentially dangerous behavior. At one, the *discipline* is more about the adult being present and disciplined in paying attention/looking out for potential hazards. A time out would not be appropriate in this case. Does she know how to modify an environment to address this?
13. If your family or theirs is out of town on vacation and the other family needs care, what's the rate expected? And how much paid vacation does the nanny receive/ how much from whom?
I'm going to stop here. As you can see, there are a lot of moving parts which need addressing. In my opinion, one of the worst things a parent can do is to go into this sort of situation dismissing the need for a written contract. A contract benefits everyone with clear communication, expectations, and a chance to state-- beforehand-- what everyone needs. In my experience, some people feel weird about bringing up contracts with friends and clients/employees. They want to hold onto the idea that everyone is friends and it'll all work out. (and sometimes, it does, however...) Those are the situations which end up getting resolved in court because no one wanted to admit, in the beginning, that there is a very real potential for there to be disagreements.