heswall the difference between a CM and a nanny, besides some EYFS issues, is location location location (and dedication to one or more children in the same family generally). A nanny is employed for certain hours in a week - they aren't generally employed "for flexibility". If the parent is running late, they should be calling the nanny the second they know they aren't going to be home at the contracted hour.
You DON'T leave it until after you're already meant to have been home, and this is especially poor form considering it's the nanny's DS's birthday and the parents know that.
Even if they have the best excuse in the world for being late, they have NO excuse for not contacting the nanny earlier and therefore giving her the opportunity to take her charge back to her house and spend her son's birthday with him.