3 year old rough with newborn

Kelly • Mommy of 6, should we make it 7?!?!

Just brought baby home and my 3 year old is clearly over the moon in love with her but she is super rough. She wants to do everything I do, burping her for instance, I pat and she whacks :/ She's squeezing babys little feet and hands and won't stop touching her head and face, especially her eyes. So far I've been trying to patiently explain the correct way to touch her but it seems like she's just not listening. Im not yelling or getting upset because I don't want her to feel like she's in trouble and resent the baby but also don't want her hurting her little sister. Any tips and advice?