I am not sure of the ages of your children OP.
I agree that as a nanny, it is important for her to play w/the children. I am a nanny and I actively engage w/my charges since I know the parents are primarily paying me for the interaction duties I perform.
However, if your children are older, at least around 3 yrs. of age or so, then it is expected that your nanny should get some breaks during the day. To expect her to non-stop play w/your children is not healthy for her since it may burn her out plus your children need to learn to self-entertain as this is a skill that every child needs to learn for himself eventually.
One thing you must understand is that your nanny is not going to do things 100% the way you do. Whomever you hire...She will always do something or other that you may look down upon as not good enough for you. It is only normal, natural and to be expected since no one's standards can meet our own.
Please consider this when deciding what to do.
As long as she is reliable, punctual, trustworthy, responsible, engaging and follows your wishes, I would thank my lucky stars.
A good nanny is hard to find and once you find the right one, things will never ever be perfect but they should be as good as can be realistically expected to be.
Hope this helps.