I can't see the rat coming out in broad daylight whilst you, your child and the dog are out in the garden. Well not unless it pulls up a deckchair and sits alongside you ;-)
It will, at some point eat the rat poison. We had one at work in the warehouse and I think it took it several weeks to get round to eating it, but it did, and we found it belly up underneath a cage (I felt a bit sorry for it to be honest!)
Unless someone who knows about this comes along, I honestly think you can safely assume it safe ot use your garden during the day.