This is weird. It sounds like their third child was previously a girl, then became a boy for some amount of time and has now become a girl again. I doubt this is the Czech meaning.
It might make sense in a very particular way of speaking for some Brits but it requires a ver specific context. It's not correct here.
I agree it should be "... Is again a girl" or "another girl". The main translation "their third child is a girl again" would nit be used in English, it suggests that she previously changed sex to a boy, but has now changed back to a girl. Can we at least accept "is again a girl"?
I'm giving it another go. Their third child is again a girl is a much clearer expression of the thought than the given translation of "Their third child is a girl again", which could imply that first she was a girl, then she had a sex change and became a boy, and now she is a girl again!