One of my sliding glass doors has a lock and key (but from the outside). Our front door requires a key to lock the bolt from the inside at night (so a key required for the bolt from both sides). I'd call a locksmith and see if there was something they could install, maybe a locking bar like a lojack for a car instead of just an easy up/down one?
My niece channeled Houdini at that age, my sister would use the halter for her in her high chair but she'd be out of it when my sister would turn around and climbing the wall behind the high chair.