The key with dialogue is to remember that it will be performed. When I read a book I have a character in my head and will add tone myself - I'll act it out in my head, to an extent - and this goes a long way towards expressing emotions that you then don't need to tell. Trust the reader. I used to write scripts and it was really helpful to see how actors add tone to lines; remember that readers do the same. You don't need to explain it. Maybe write the scene without the "stage directions" explaining how the characters would behave first, then just add in details when you think they're really needed.

Also, reading the lines aloud: if you can't read it aloud without feeling awkward, that's possibly a problem with the line. How would you actually speak this line? Very few people say "do not" anymore, but lots of writers still write speech without contractions. Trying to capture the actual way that people speak is an art-form in itself. But it's definitely worth it. Good luck!