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This is perfectly normal. Mine take it a step further and try to lay eggs on top of one another.
To encourage laying in both nestboxes, try placing the equal amount of golfballs or fake/wooden eggs in each nest box. They'll see the wooden egg or golfball and think another hen has already layed an egg there and it is deemed "exceptable" to lay their egg there as well.
As for the broody part. Best thing to do with a broody hen is to place her in her own area. I keep my broodies in a medium sized plastic dog crate inside our coop/run. This allows the hen to have the comfort of being near her companions but also the privacy a broody desires. Not seperating a broody, lets the other hens to continually lay in the clutch she is sitting on. Therefore embryos begin developing at different times, leading to a "scattered hatch"(all eggs don't hatch same day). Scattered hatches do not do well and are often messy and heartbreaking. So, best thing to do is seperate any broodies and not use a community nestbox(unless you can keep the others out of it).
-Kim