btw I also have an opposite story which I’d like to share:
I hired a nanny recently, a wonderful old lady who was very kind and friendly to my daughter. My daughter (aged 3.5) called her “granny” and felt she could get away with anything when at her place. She threw things all over the place, shouted, screamed, generally wouldn’t listen. When I went to pick her up, she’d be an angel and the only hint I got was that they kept asking me for more corn flakes all the time. Turns out she was throwing them about, not eating them. I caught my kid misbehaving a couple of times and made her apologise, but the nanny insisted that I shouldn’t be strict, everything was fine and so on. They rennovated their place and my daughter (a generally wonderful and obedient child with me) scratched the walls and so on. By the end I was sure she was not behaving herself, and I kept asking the nanny everytime if everything had been ok. She still wouldn’t tell me. Then one day she just called my girlfriend crying and said she wanted to quit.
I’m not saying this is relevant in your case, since you apparently spoke to the father, but it is sometimes possible that you get off on a bad start with a child who would otherwise be easy to control. They can be quite devious at that age, so it is important to talk to the parents about everything (though it’s usually the parents who have lost control and the nanny that has to make things right).