Ants.
They didn't just appear and lay those eggs, they already have a nest in your house. And the bigger ant is another worker, it's bigger because it ranges farther then the nursery ants that are tending to the eggs. A queen ant would have wings, and once they shed their wings they stay in the hive.
@Bigbill is right, something has disturbed the colony.
I had the same thing happen about 25 years ago in my old house. The ants got in through a crack in my stucco and created a nest in the wall. I didn't know they were there until they came out from under the window sill and swarmed in my living room. The intelligent and always resourceful Ms. Henderman grabbed the vacuum and sucked them all up before they got too far.
You have to kill the queen to get rid of the nest. Topical sprays will just kill the workers it touches and the queen will be left alive to produce more workers. I used an ant bait, it is poison on corn meal that the workers take back to the queen. The product I used was Grant's Ant Bait but I'm not sure if they still make it.
Good luck!
