I too think your neighbors birds may be eating their eggs due to poor nutrition. If they are given sufficient protein and calcium they are likely to stop eating eggs. I would suggest feeding a 20 percent protein feed such as Purina Flock Raiser with oyster shells on the side. Layer food does not have enough protein or calcium for some birds and these girls need a little catch up. Also use hard fake eggs in the nests.
Hiding places with out getting trapped, and extra roosting places will help with integration. Try to let them work it out on their own. If you want to try the integration, add all three birds at the same time
Hiding places with out getting trapped, and extra roosting places will help with integration. Try to let them work it out on their own. If you want to try the integration, add all three birds at the same time