Hard situation with step daughter and bio daughter

We haven’t been able to figure out why, but everytime my 3 year old step daughter comes over, she hurts my 1 year old daughter. It’s gotten so bad that she has shoved my daughter off a king sized bed, kicked her in the head, shoved her away, rolled her ankle under a sit-in play car door, and as I’ve seen these things happen, it’s very obvious she WANTS her to get hurt. She literally laughs and smiles until she thinks someone’s paying attention and then will cry cuz she knows she’s gonna get in trouble. We have tried EVERYTHING ranging from talking, time outs, taking things away, trying to bribe(not my idea) and spanking. NOTHING has worked. And I’m at the point where I have threatened to kick her out before she seriously hurts my daughter. She’s already given her a concussion. What can I do? Her father obviously doesn’t like the idea of me kicking her out and says that if I do then he will leave with her, but if NOTHING is working, am I expected to just sit and allow her give my daughter brain damage cuz she can’t control herself?!?! It is so hard to love that child when she is acting like a pure evil little brat. And it’s creating so much strain on my relationship with my DH because is coming Acrossed like he’s rather protect her sensitive little feelings rather than protect the child getting hurt. What should I do....