I'd be more inclined to put the female and chicks in a very small, contained area (like your lovely set-up there) as chicks can wander off and be unable to find their way back, especially in the dark. The male takes on the role of retrieving lost chicks, while the female takes care of the majority. If one wanders off in a large-ish area she will not go and retrieve it if she's a lone parent.
Once the chicks are about 7 days old they should be strong enough to get back to their parent without worry that they will chill before they get there and you could give them a bigger space. You could add a heatlamp just in case as well if they are being dippy and not staying with their mother. You may have to ensure the male can still see his mate or he will drive you bonkers with his calling. I'd wait and see how he does before making the decision to separate them though.