Yikes that is a tough one. What will you do if she pushes the younger girl into the coffee table or down onto a toy and you have to explain to the parents why the younger child has a bruise or goose egg?

Do you put her in time out or give her consequences when she gets aggressive and tell her that it is not okay to push and hurt others?

If you really don't want to terminate then you will have to watch this girl like a hawk or have her constantly at your side so that she won't have the opportunity to even be aggressive.

Be firm because you have to nip it in the bud before something more serious happens or it escalates.