I think those were an eggs of a Bluejay bird. Blue jays are sometimes known to eat eggs or nestlings. This maybe the reason why only two eggs were left when you took another picture or maybe your daughter was right on her speculation.

Thanks, Jordanwalker, for responding to my question. It makes a lot of sense that those are the Blue Jay's eggs. They seem too big to be the Cardinal's eggs and we have a lot of Blue jays here.

The missing egg theory is interesting and it's kind of scary too for them to eat their own eggs/nestings! In some ways I'm not too surprised too as they're pretty aggressive birds. One Summer, they built a nest over out garden arch and three little birds hatched. The parents were very protective of them and kept sqawking at us whenever we walked under the nest. They always bully other birds including the Cardinals that regularly visit our garden. The Cardinals aren't aggressive, but they sure are brave enough to not to give up their ground easily.

Cardinal eggs usually number from 2-5 per nesting and are whitish marked with browns and greys. Their nests are twigs and grasses at low to mid levels located in thickets or bush. Blue Jays eggs number from 3-7 and are blueish to greenish. Nests are cups of grass and or twigs and are built at mid to upper levels of tress. Yes, birds do dispose of "bad eggs" and Blue Jays can be carnivorous if food is scare. Native birds will also fend off or kill of babies of species that are non-native to the area (such as sparrows as these migrated over on ships centuries ago). Have fun birding!