When you're in "serious" mode, what words are you using? It's great that your tone of voice, expression and body language are in agreement, but is your pattern of speech different too? Usually super.short.phrases work best w/ my DS in those situations.
But what I'd recommend doing the rest of the time (in calm, playful moments) is doing lots of emotion theater: role playing (with both of you taking turns at making different expressions), using stuffed animals or puppets to demonstrate what actually happens and how it upsets you, then using them to model how you really want her to react; read lots of books about emotions, and just talk about/identify emotions.
Also, talk a lot about your expectations--how you expect her to behave in certain situations; then, remind her right before you enter those situations. Decide beforehand what the consequences will be be, tell her in advance, remind her, then follow through (ex: hitting at a playdate? go home or end the playdate as an extension of people being hit don't want to be around the hitter)
My 3.5yo DS is also super sensitive to my emotions: "Mommy's mad/frustrated. Want Mommy to be happy!" is rather common around here. But DS listens to me pretty well before it gets to serious mode (most of the time), so a simple, "Stop xyz," or "Gentle touches," reminder is all he needs. When he keeps doing the undesireable (such as repeatedly crashing into me with his tricycle), though, I'm usually the one who needs to calm down, so I separate myself from him (might just be by a few steps), which he doesn't like.
It sounds like your DD is just very secure in your love. Just keep practicing empathy, and eventually it should click.