"........plenty of native critters and woodland birds .......". There you have it, Denise.
Virtually any animal that can break into, swallow or carry off an egg will do it any every opportunity.
For some critters it's a random chance for a nutritional boost. For others, it's an anticipated annual food source.
Mamma pushing the eggs out is unlikely. That would draw predators to the nest and birds take great pains to avoid attention around their nest.
Perhaps you have noted that there are never egg shells around an active nest or perhaps you have seen birds flying with egg fragments for distant disposal.
Many animals that we think of as vegetarian will readily eat flesh and eggs when available.
Snakes, Squirrels, Bluejays and Starlings are just a sample of the smaller villains. It's a long list.
Fortunately, lots of birds routinely nest more than once each season. They can re-locate, re-nest and still have a successful season.