All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The fact is as you mentioned that some scholars did indeed forbid a Muslim from working as a hired person for a non-Muslim in matters that involve humiliation of the Muslim.
Hence, if the woman's work as a nanny for the children of non-Muslims involves this forbidden meaning, then it is not permissible.
We have some Fataawa in this regard in our Arabic site which are as follows: 156231 and 242179.
You may also refer to the following Fataawa in our English site: 245635 and 81686.
Allah knows best.