WOW, you do have your hands full.
You do need to have a sit down with the parents and decide on a plan that all can be on board with. It is not that unusual for an four year old to have a challenge with number two, there is often fear and it is an uncomfortable feeling. Another thing as you are new to the family this four year old is overwhelmed with trying to please everyone. There is the stress of a new baby, school and a new nanny, this is allot for a little guy to process. It is true the parents should have been upfront about where the four year old was in potty training development but you also need to know if you are a professional nanny and you sold yourself to the position as such the parents might not have worried about you being able to handle the challenges of their home.
This is your call but if you are that upset then you need to communicate this with the family, the four year old most likely senses your stress and this will not help.