Hi A.-
I was a Nanny for many years, and I know how hard it is to bond with kids. It takes everyone a while to get use to each other and love each other.
It sounds like your kids have recently lost a wonderful nanny, and I'm sure they are feeling it would be dishonorable to their old nanny to be friends with their new one.
I worked with a family for years and every morning one of the kids would give me a dirty look first thing in the morning. Not to be mean or that she didn't like me, just I was not who she wanted to see. When the nanny is home, that means Mom won't be.
If you like your new nanny and she meets your needs, the bond will develop between her and your kids, it just takes time.
To help, I suggest having the nanny take each child out for a fun day just the two of them, so they can bond. I would also share stories about my life with the family to bond. Maybe the new nanny should bring in family pictures or other personal items.
Best of luck. I know good nannies are hard to find, (I helped a friend hire one a few years ago, and it took a while!), so don't give up.
R. Magby