Allowing her to drive? Come on now... I think you might be hunting for reasons not to allow this. Adult women do not need their husband's permission to be allowed to drive. He isn't controlling her by allowing her to drive... he would be controlling her by NOT allowing her to drive.

Plenty of women are driving 3 weeks after birth. I am 3 weeks post birth with a newborn, and a 3 year old, and I'm fully attentive while driving. If you feel unsettled about her taking your child to swimming lessons, be honest with your ex DH and yourself about WHY.