It happened with us too as soon was we brought her sister home. It took a good two months of the intense meaness and another 4 months and counting of slowly making things closer to "normal" (pre sister). As the others said, consistent discipline. I use "break time" I found a spot the works for my daughter to have break time. If she harms anyone in any way (biting, hitting, throwing things, kicking)or talks back which started with her sister's arrival, I carefully put the baby down in a safe place. I pick up my oldest without looking at her and quickly get her to break time while I tell her "It is not ok to hit people when you are upset." I set the timer for two minutes. When the time is up I have her look at me and I tell her that if she is upset she needs to use her words amd tell momma that she is mad or hurt or....instead of hitting and then she must apologize to whomever she hit usually its me or her sister. There have been a few days where we have done tthis 50 times and I thought I was going crazy and it wasn't working. But with a bit of support from experienced friends I stuck it out and it did work for us. The other thing is that she cannot leave break time if she doesn't apologize. So, I continue to ask every couple minutes, when she refuses, if she is ready to say she's sorry. and there have been a couple times that she stayed there for a half hour or so.
Then there is the whole part about including your oldest. It is important and it is also important to give her time alone with you , however almost impossible with a new born. My daughter refused those attempts about 90% of the time at the beginning and she would not allow me to do a puzzle or read a book to her if I had her sister at all. But I continued to offer over and over and now she will alot of times. Fortunately, I had my husband to help out.
I am glad we aren't alone in this. For a long time we were the only ones in our circle of friends who experienced this and I really thought we had a long term problem but I don't think so now.