I concur with Tyler. Rotten eggs are no joke and will only get worse if left alone.
If you have to do anything with a broody hen (or any
chicken really) the best time to do it is after dark. They tend to be pretty catatonic then and it's much easier to move them around. Broodies will still be a bit irritable but it's much more manageable.
It would also be a good idea to candle the remaining eggs to see if they are viable. Once one egg goes rotten, it tends to spread quickly to the other eggs. If you can remove any of the eggs that are clear or obviously dead (no veins, large red or greenish blotches freely sloshing around, red ring), it will reduce the chance of more of them going bad.