Insurance between jobs?

We are currently covered under my wife's insurance. We are moving for my new job which I have been told my insurance will be effective July 1st and they will accept my wife who is due with our first child in August. Her insurance will end June 16th. So we have about a 2 week lapse. I know typically you have approximately a 60 day grace period to elect for a COBRA. If anything happens before we choose to elect for COBRA will it be retroactive? I'm thinking there is a good chance all will be well for a two week period (my wife's dr appointments are 2 weeks apart they way it is now) but definitely don't want to risk my wife and child. Any suggestions?