I would start off by what you stated in your post OP, then perhaps inquire about the reason the position ended.
I wouldn't ask anything too personal about the prospective family as you don't know whether or not the ex-nanny will report how the conversation went.
Offering references is a huge plus in my opinion, this usually means that the family is in good standing w/previous employees which definitely bodes well for them.
Hope you get the job!
Good luck!
