Answer:
She and David (subject) went to school. The teachers taught her and David, or David and her (object), to read.
A compound subject can never have "her" as the pronoun.
TIP: It's really much easier to use proper names when making a compound noun.
Example: Sally and David went shopping.
But, alas, there are times when we must use the pronoun.
For example, in a conversation, a Mom asks:
"Where is Sally?"
"She and David went shopping."
TIP: Anytime you are unsure of the pronoun to use in a compound noun, remember that the sentence must be readable with one and both.
As examples of splitting up the sentence to use this tip:
Wrong: Sally and her went shopping.
Right: Sally went shopping. (remove one in the compound noun)
Wrong: Her went shopping. (remove one in the compound noun)
So this tells you the right way would be: Sally and she went shopping.
(Remember, though, "she" must be defined in a previous sentence before using the pronoun.)
Wrong: Him and Sally went to the movies.
Right: Sally went to the movies.
Wrong: Him went to the movies.
Right: He went to the movies.
So this break-down tells you that "he" should be the pronoun in a compound noun.
Correct: He and Sally went to the movies.
Correct: Sally and he went to the movies.
Again, it may be far easier to define the pronoun and use the proper name.
Correct: Sally and George went to the movies (or George and Sally).
Wrong: Sally and them went out to eat.
Right: Sally went out to eat.
Wrong: Them went out to eat.
Correct: Sally and they went out to eat. (as long as you defined "they" before)
Here it may be easier to assign a noun to "they". For examples: Sally and her friends; The family and Sally; Sally and her friends; The students and Sally; Sally and the students; Sally and the other students...