P.W.
As others have said, you are an employee of this family and not part of the family itself. They have no obligation to attend your children's parties or to have you attend theirs. If they have, or invited you, in the past; then consider it something above and beyond what usually happens.
Make sure to keep your relationship professional. The family should be paying for your gas on any work related errands, or at least reimbursing you. You should also have some sort of written contract.