Old sibling dilemma

So my oldest (3) flat out has said she doesn't like her sister.  She won't hold her, only kids her or hug her if I ask her too, and most of the time tells me no.  My mom says I'm pushing it too hard and that it will come over time.  Are there any other moms having this problem?  I just don't want to feel alone in this right now.  On Facebook everyone posts these lovely baby and toddler pictures and I can't even get her to be that close.  Is this normal?