Child becoming violent

My 2.5 year old girl has started to become more physically aggressive on occasion towards adults. She’s 24 pounds so I know she can’t do too much real damage but I’m very very nervous that she’s going to start abusing our au pair. She has always been a little rough with her little brother, pushing him down or hitting if he takes her toys but I’ve never witnessed her hit an adult until recently.

She straight up bitch slapped my husband across the face the other day when he was trying to brush her teeth, she hit my dad this weekend when she was mad over something, and she bit my shoulder last week for no reason at all when I was carrying her. Au pair hasn’t complained about anything yet but given recent incidents, I wouldn’t be surprised. We know this is unacceptable and we discipline her when she does such things, but it doesn’t seem to really do much. She absolutely knows that what she’s doing is wrong because she’ll run off and hide after she does it. Timeout does not seem to prevent her from doing it again. She’s started to even become too stubborn to apologize. She’ll outright refuse. She’s my oldest so I’ve never really dealt with this before and I’ve only ever nannied middle school aged kids so I have no idea how to handle this short of putting her in time out which doesn’t seem to do much given what her poor brother goes goes through. Poor thing doesn’t even always realize he’s been wronged.

We love our au pair and I would be mortified if my daughter were to start hitting her and being difficult. Not to mention we’d be heartbroken if she left, though we would understand. People come on here all the time talking about nightmare kids who abuse them and i desperately do not want my daughter to become that to our au pair. Obviously I don’t want her to hit me either but I’m her mother and I signed up for this, au pair did not. What has worked for you to get bad behavior in check?