hi IANAL but i find your post quite interesting. I speak as a grandmother myself.
Firstly you speak as if you are the guardian of your child, is that the case?
I realise that the mother is young but actually it is her, not you that is the concerned party, in any legal proceedings, unless as above you have the legal status as a guardian.
As for the “Nanny” she is of equal moral and familial status to you, and is a grandparent too.
As she has been nominated by the Court to supervise contact, i can only assume that she is not a risk to the child.
It seems to me that the person who really wants a relationship with this child is the nanny, and the only way for her to do this is via her son, hence her “forceful” approach.
Have you considered ( as you seem to the person in control) nurturing some kind of relationship with your counterpart the nanny. Whereby your grandson gains the benefit of two active grandparents, a special thing.