“After that, you can do whatever activity you want with him.”
Although that seems like a win, it's a lose-lose situation in disguise. If your nanny does whatever she wants with your child — color, watch an episode of their favorite show, take a walk — chances are she'll then be asked what they did later and get the "Oh, well you could have/should have done this" follow-up. It's important to trust your nanny to do fun and educational things with your child, but if you have opinions about what types of things they should do together and when, you need to be clear. Most people work better with clear expectations.