Call an exterminator. If it's a few ants, regular ant spray from the store, taking care of the dirty dishes promptly, and moving the trash can away from the door will do it. But if it's a lot, like it sounds like, you gotta call in the professionals.
The exterminators are safe. If you're concerned, you can just keep the kids out of the room while they're spraying and maybe for an hour afterward. Go out on the deck with baby and play outside while they spray and for awhile after, or go run errands as soon as they're done.
I use Milberger Pest Control and have had good luck with them. They sprayed my house for ants and my attic for silverfish a couple weeks ago. They're careful not to spray the kid's toys and not to make a mess. They also offered some advice on yard maintenance to help keep the ant problem down. They said ants were really bad this year.