You definitely want to do whatever it takes to get some occupational therapy. I'd also take her to the dev ped AND the ped and discuss your concerns about her behavior. If it does come down to a CPS investigation (and sadly, it does more often than you might think), you want to be on record with as many professionals as possible as the first person to bring it up. Not to scare you, and it probably won't happen, but my son's service providers have saved my butt a couple of times.
If your daughter has a diagnosable condition (ASD, MI, some other developmental/social/emotional something), then traditional discipline methods won't work, which may be what you're bumping up against right now. For my three eldest children (all NT), I let them have their tantrums. With my youngest (definitely NOT NT), I couldn't do that because he actually hurt himself. Sibling conflict in that case is more about your older daughter's inability to process stimuli appropriately than about just being bugged by her sister.