Toddler jealous of sibling.. help!!

My pediatrician was not much help with this. 2.5 year old daughter jealous of 13 month old daughter to the point of hurting baby- hitting, pinching, pushing her over, screaming at her. Older daughter very verbal and intelligent, does not behave like this with any other children (cooperative and sweet). Has anyone else experienced this with a positive outcome? Discipline and redirecting seems to have no effect (“hands are not for hitting”, “we don’t hurt baby”, special mommy time, etc). I separate the two of them but the moment they are together I am hauling an angry toddler off a screaming baby. I am so stressed that baby will get really hurt. Please help 😭😭