So, you were told that your son needed to be picked up by 4, and did not pick him up. Many daycare centers would have called Social Services when you did not pick up your son when the daycare closed for the day (at 4). Instead, this woman just took your son with her to her family event. You should thank her for continuing to care for your son AFTER her business closed for the day. I know a non-profit center in my town that gives you 15 minutes after pickup time to pick up your child (at $5 per minute), after 15 minutes, the Child Protection Officers arrive to pick up your child.

If you had a problem with transport, in my opinion, you should have enrolled your child somewhere that did NOT want permission to do so. I understand your frustration that you feel your wishes were ignored, but you should not have assumed that failing to sign a permission slip conveyed your wishes, nor that it was acceptance by the provider of your wishes.

I am no attorney, but I would guess that since you gave no notice, you're going to be sued for 4 weeks tuition, and will probably lose.