MB here - I wouldn't do this to our nanny in a million years!!! That's awful!
They had notice, and if they had the slightest idea that they might not be able to get the time off themselves they should have made alternative arrangements. Why can't they pay for a temp nanny for the week?
If it is not a disaster for you financially to be unemployed after your vacation, assuming they fire you for going, then just go and start looking for another job when you come back.
If you can't afford to be unemployed, try to explain to them why cancelling your vacation is a huge problem for you & yoru husband and that you felt you did everything possible to make it as easy as possible for them, i.e. plenty of notice. If they insist that you don't go or they will fire you, tell them they need to compensate you for any expenses incurred. And, start looking for another job right away, they don't sound like very nice people.