If June 7th is the day she really did start to incubate them (she could have been laying her clutch still and NOT actually brooding on that date) then they would be due around today. Goose eggs take between 28 and 35 days to hatch, yours would take closer to 35 days due to it being a larger goose. After the incubation period is up, it can take like 3 MORE days for the babies to make it out of the egg.
Yes, next year she needs to be separated in order to sit on her eggs. Too many distractions like your other birds bothering her contribute to incubation problems. Just as a side note, broody birds will kick the dead eggs out of a nest because they know who is alive still and who isn't. So if she kicks the same egg out a second time I would be wondering about the viability. Some hens are just stupid and lay way more than they can sit on, then have eggs all over the place....
Yes, next year she needs to be separated in order to sit on her eggs. Too many distractions like your other birds bothering her contribute to incubation problems. Just as a side note, broody birds will kick the dead eggs out of a nest because they know who is alive still and who isn't. So if she kicks the same egg out a second time I would be wondering about the viability. Some hens are just stupid and lay way more than they can sit on, then have eggs all over the place....