Should I remove zebra finch eggs from the nest a nestling is in?

I have a pair of zebra finches. They hatched an egg (for the first time) about two weeks ago. The nestling is doing well. I thought the parents would not lay eggs until the nestling was out of the nest. At which point I intend to pull the nest out so that the parents will rest. The nestling is still in the nest, and now there are suddenly two eggs with him/her. Now the mother finch has a bald spot. Should I remove the eggs from the nest? I would love an answer from someone who has experience breeding zebra finches.