Translation:Both the woman and her daughter are reading the letter.
"Die Frau und ihre Tochter lesen den Brief" is not wrong, but it's missing the emphasis on the fact that they both read the letter. That's what "Sowohl... als auch.." is used for.
A sentence with "beide" could express that, but only if you emphasize the word when you read it out loud. You could say: "Die Frau und ihre Tochter lesen beide den Brief" or even "Beide, die Frau und ihre Tochter, lesen den Brief".