Ha ha ha, ya gotta love that look on your goose's face, she doesn't look pleased to have gotten her photo taken! What kind of goose is she? I have a pair of Embdens, the goose has been laying & I haven't been collecting her eggs, hoping she'll go broody. So far she hasn't, so I'm considering collecting any new eggs she lays so they don't go to waste.
Congratulations to all the hens hatching out chicks, and to the others with developing egglings under them. Way to go Mamas! My broodies stay with their chicks for about 5-10 weeks, some leave them earlier than others. They begin to lay again soon after leaving their chicks and returning to their flocks.
In all the times I've had hens incubating eggs & hatching chicks I've only had one egg that seemed to have "exploded" because it went bad. And even then it wasn't such a big mess, it was easy to clean up & the other chicks hatched out fine. All the other times the undeveloped eggs stay intact and I toss them out after the Mama has left the nest with her hatched chicks.
So that's why I don't bother candling the hens' eggs. Sometimes they will push them out because they're not developing, sometimes they push out developing eggs for unknown reasons. Perhaps it was avian error, perhaps the voices in their head told them to, who knows? But I don't worry about spoiling, exploding eggs in the nest.
I have a hen who has been on her nest for almost a week. Last night I found a broken egg on the ground outside her nest box, and when I checked under her found a broken egg at the bottom of the nest, egg goo covering her other eggs and the skin on her breast. So I wiped all the eggs with paper towels, cleaned the nest and replaced the gooey straw with dry fresh stuff, then put the hen back in place with the eggs underneath her. But she didn't want to set on them anymore, and seemed to have spent the night on the roost. This morning I opened her cage to let her out, then I had to leave for the rest of the day. I was surprised to see her back on the nest when I returned tonight. I had thought she had quit the job. I was going to swap her eggs for fresh ones tonight, but took a moment to candle them. There was veining & tiny curved embryos visable in most of them. So as an experiment, I left them under her, and plan to candle them again in a few days to see if they are indeed growing.
Sometimes all you have to do is look funny at an egg and it won't develop. Other times they can go through freezes & floods and still hatch. Go figure...