I'll be frank with you. I apologize if I sound harsh, I don't intend to be mean, but to me, it's the truth. The only reason she acts like this is because you allow it. Sometimes it takes more than a time out, such as toys taken away, or other consequences. I am a mother of 4 children, 3 boys, one girl & I am firm with them because if I don't teach them to respect me, or themselves, they will struggle all their life with it. Others will not want to be around them and they'll be in horrible marriages simply because they do not respect their partner or themselves. Of course, I'm talking in extremes here, but sometimes the extreme in the mind needs to occur to get the control reversed in the home. It may be a battle, but it's one you need to win. You can do it. Trust yourself. You owe it to her & to yourself to get it under control. She's acting out for whatever reason. The goal is not to get to the reason, that can come later. The goal is to teach her self control and self discipline. Yes, it can be done with a 16 month old. Kids do not take initiative themselves. That's why they have parents. Good luck to you & I'll be praying for you.
I felt like I should add a few more things. I really hope you don't take this to mean that you are a bad mom, because I don't think that, and you aren't. You care enough to ask for help. Your daughter is lucky to have you as a mom. I'll share my own experience. My first son, who is now 10, was a terror when he was that age. My doctors told me he was going thru his terrible two's early and that meant it would end early. Needless to say, they were wrong. It tried my patience day in and day out. I nursed him, and then stopped when I went back to work. He wouldn't sleep, screamed all the time, and would throw things & hit others. Of course some is chalked up to he's a kid, but I really struggled at having a child that was mean. I had to learn how to teach him self control, and disciplined him with something that worked. He hates it when his stuff would get taken away. So that's what I did. It was nothing short of hell, but now I have a much better behaved son, hormones and all and I am still firm with him, teaching him discipline as I do all my other kids. Just remember, there is light at the end of the tunnel & you can do it. I taught him sign language like please, thank you, and yes mom. That helped a lot at developing his confidence, our communication and taught him to use his manners also. Maybe try that??