My daughter speaks fluent English and learns Chinese in school. But we don't speak Chinese. n this case, is it essential that she takes extra classes in Chinese?

Chinese language can be challenging in Sch setting esp for children who doesn't interacts much with it. Having extra classes depend on whether the child wants it or not. No point letting her attend if there is resistance. Learning the lang thru play or fun way can engage their learning in future. Get ur gal interested by teaching u and ur hub and keep affirming her.