Is this sentence grammatically correct? Charlie is angry about moving, but her mother is excited.
This quote is grammatically correct. You even remembered to include the comma before the conjunction “but”!
This is a compound sentence. It is made up of two independent clauses combined with a conjunction (and a comma).
Independent clause 1: Charlie is angry about moving
Independent clause 2: her mother is excited.
The reason this sentence is correct is that both sentences are complete sentences. Notice that they each have a subject and a verb. They each express a complete thought. Your sentence is also clear. I know that Charlie is angry, and I know what she is angry about. I also know that her mother is excited. Because of the word economy of elliptical clauses, I know that her mother is excited about moving also. The sentence would be awkward if you included “about moving” twice; the reader knows the clauses share the cause prepositional phrase modifying the noun angry.
When writing an essay, it is important to remember that your thoughts are center stage. Your ideas are the important ones.
This type of writing is devoted to the presentation of the writer’s own ideas and generally addresses a particular aspect of the subject. (eNotes, Essay)
Therefore as long as your sentences are clear, you are on the right track. Grammatically correct sentences are a good place to start!