Instead of having her entertain the baby, have her help with the baby while supervised. My oldest was 2 years old and he wanted to do everything with baby but he was rough too. I set up a time and environment where he could "help" and spend time with me and the baby together.
I put him in the middle of the bed with pillows all around and had him hold the baby and feed the baby a bottle (expressed breast milk). The baby was all snuggled in pillows and sitting up in the right position with the pillows and just sort of adjusted to be across his brothers lap. It was a moment I won't ever forget.
She is older but do something similar. Let her help change the diaper, put her on the couch (after washing hands) and lay the baby across her lap. This way she can't get up and "be rough". When I let younger kids hold the baby on the couch I put pillows all around on the floor, this way no harm no foul if accidents happen.
Lastly, be gentle with her, show her how gentle you are with the baby and in all things. Don't yell at her our get tense, she doesn't know how to deal with a baby, its your job to smile and correct her calmly and show her how to do things the right way and give her alternative ways to express affection. Let her know that you want her to spend time with the baby and she is a great sister! Let her know how scared you were and problems you had when you first brought the baby home and how you too had to learn how to treat the baby. Tell her how you learned to do things the right way, by asking!