I have a 9 yr old, 6 yr old and a 2 yr old. I also have a Masters degree in Psychology.
Find ways to say "yes". When she does something she wants that you are fine with, then make the effort to point out to tell her, "yes". She is learning what is acceptable and what is not. It sounds like hitting is a big no no for you, that said, if you believe in spanking this negates your rule of not hitting. For a one yr old this is confusing. Consistency is very important. So if you do NOT believe in spanking, then you will need to teach her that hitting is NOT the way to let out her frustration and anger. For a 16 month old, you can start using time out, but you should see if it is something else bugging her. You can also redirect like other said or take away her toy or changing her scenery. Also check to see if she is teething. Teething is a big culprit for making them cranky. Those teething tablets really work great and teething gel you apply with Q-tips work great too. My poor son was getting his molars at the time, and I didn't realize it until it was days later. When you use time out for your 16 month old, you have to use this very little and immediately. If there is too much time between putting her in time out and her hitting, it looses it's effectiveness. Same with using it too much, so only use it as a last resort for a toddler because they do not understand time as well as older kids. When my 9 yr old called her brother stupid, I immediately put her in time out. Choose one or 2 places in the house for time out that's away from toys, tv, and computer. For a 16 month old you will need to be near by and see if she stays in the spot. Mine thinks it's a game. I put her back 3 times and wait to see if she leaves again. For your 16 month old is she comes out of Time out, put her back in and say, "No hitting! Stay in time out" at least 3 times. If they are crying, you can console her for a couple of seconds and step back within 5 feet of her. You'll need to say it again when they are calmer since they can't really hear you when they are upset.
I have to mention that my husband would hold my son in time out because he wouldn't stay for the 3 or 4 minutes when he was 3 and 4. It really helps when your spouse and you are in agreement. It's one minute for each year of age, so 2 minutes for a two year old. I round down for their age so not quite 2 then still one min. One more thing, when my 9 yr old was 2 yrs old she would have these terrible tantrums. I couldn't safely get her to time out. So if it was in the Kitchen, I'd try to move her to the carpet away from furniture and toys. I'd tell her to go ahead and when she was done I'd try to talk with her about why what she did was wrong and what I wanted instead. You need to give them opportunities to correct their behavior as they get older, so they know what is expected of them. She is now 9 yrs old and still has a tantrum now and then, nothing like before, but I have to handle her differently because she is older. I have more leverage now that she is older because I can ground her from TV, computer, her iPod, and her hand held video games. I take them all away, and I warn her that if she chooses to continue to act this way, then she will be grounded for additional days. When she sees that her brother is not grounded, it is a huge incentive for her to rethink her behavior. I also tell them that they can choose to behave properly or be grounded, I tell then, Don't give me a reason to ground you. When they are doing the big no, no's, which are hitting/biting, name calling, and whining, I put them in time out.
I hope this info helps. If you let it go when she is 16 months, the behavior will only get worse. Keep that in mind when you are doing this. I'm not perfect, but I found the more consistent I am at using Time out, the better it worked. I also started earlier with my 2 yr old and that for those big things and let the little things go. I know you get tired, so keep trying; it will work in the long run. Good Luck!