In my opinion, a nanny's task is to "Help the parents by helping the child(ren) in the manner by which the parents want to raise the child(ren)."
I'd also make one more presumption: When the parents interviewed you for the position, they expressed some of their desires on how to raise their child.
That being the case and with the information you've exposed in your question, I think it's safe to make some assumptions:
- These parents clearly care about their child
- These parents clearly care about their child's development and success
What I definitely can't assume is if you are aware of their frustrations (we don't always share those upfront). Perhaps the mother feels like she works too much and can't -- as much as she wants to -- establish a complete schedule for her child. In this area, could you help?
Based on what you've written, it may behoove you to sit down with the parents and ask what else they would like for their daughter. Ask what they would like to see for her and wish they had more time or opportunity for. By getting them to tell you what they want, you may be able to find that what you're hoping for is the same thing they are hoping for and then you will have an opportunity to offer assistance. Having such a chatty conversation may also allow you to drop in informational comments about regularity of schedule or any other things you see can best help the child. Since they love their daughter and clearly want the best for her, they very well may adopt the idea -- and, an idea we feel is our own is one we feel we own.
If the parents feel that you are helping them in helping their child in the way they want their child to be raised, then they will feel that you are truly fulfilling the role they hoped for, even if it wasn't the role they were able to best-express initially.