Do you try the whisper technique, as she gets loud, the lower your voice goes? Making it a challenge in using her 'quiet' voice?
My kids are loud, regardless. It's when whiny comes in, then they know they aren't going to have me cave.
My oldest, used to have these temper tantrums from Hades. He seems to have finally outgrown them, at 10.
Sounds frustrating that your daughter wakes up the sleeping baby.