"My 2-year-old is doing the "I want you Mom" thing and then 2 minutes later she is on the floor screaming and crying for no reason. Is this normal for a child to do knowing that her mom and dad are not together and there is a step-parent in the picture? She even cries when I yell at her to stop something. I think I really scare her with the yelling. Am I wrong for yelling at her?"
If you think you're scaring her, then you probably are. Everyone yells sometimes, but if you feel like yelling is your main form of "discipline," you should reevaluate how you're communicating.
The common-sense question to ask yourself about anything you do to or with your child is "Would I want to be my child in this situation?" That doesn't mean that you always do the pleasant or easy thing, but it does mean you do the thing that makes your child feel safe and understood and empowered to act responsibly. If you think you wouldn't want to be on the receiving end of the yelling that you do, then you know you need to stop. (We can go back to Hedra's "Safe, Respectful, and Kind" rules, too. Excessive yelling is neither respectful nor kind. Also not safe, because if you yell all the time and she tunes you out, she won't pay attention when you yell at her to watch out when something's about to hurt her.)
I don't think your being separated from your daughter's father, or her having a step-parent has much to do with it, assuming you all get along and are respectful of each other and she has consistent rules in both houses. I think what's probably making her scream and yell so much is that that's how you talk to her. She gets clingy because she wants your love and closeness, but then when she gets frustrated, she yells, because that's how she sees you handling your frustration.
AN IMPORTANT NOTE: I'm not implying that I don't yell at my kids. I do, but when I find myself yelling I know it's because I'm feeling at my limit. I yell when I lose my shit. It rarely accomplishes what I want it to. I think it bears repeating that you have to take care of yourself and try to manage your own stress level or you won't be able to parent effectively.
The only way to really stop yelling is to 1) avoid getting into situations that make you want to yell, and 2) have another plan in place for what to do instead.
To do #1, you're going to have to pay attention to when you yell. If it helps, write down the times and situations in which you yell for a couple of days. This is going to tell you what your particular yelling triggers are. Once you know what makes you yell, try to figure out some other way to sidestep that situation so it doesn't escalate to yelling. For example, the thing that makes me yell all the time is when we need to leave the house and my older son won't get dressed. Knowing that, I can avoid the yelling trigger by making him get dressed first thing in the morning, and helping him choose clothes and put them on when I'm not under time pressure.
Yes, this takes a lot of analysis and thought for a week or two, but it's going to help you have a happier household for a long time to come. (Now if only I could stick to my own areas of improvement!)
For #2, the first thing I'd do is institute the Safe, Respectful, and Kind rules. She's still a little young to really understand the ramifications, but it's been amazing to me how easy it was for my 4 1/2-year-old to go from ignoring my requests to stop doing something to answering the question "What are the three rules?" with "Well, it's not safe or respectful, so I should stop." And then he actually stops. If you can start presenting things to her through the lens of the three rules, soon enough she'll be able to make those decisions herself. At the very least, it lets her know that there's a reason for your wanting her to stop doing something, not just your arbitrary whim.
The next step is to figure out what will help your daughter behave the way you want her to. Is she too tired? Is she feeling lonely and wanting your attention? Did she have too much excitement and/or sugar that day? If there are things that would help her act better, figure out how you can help her fix the underlying situation so she's able to control her behavior better.
If none of that helps, then distract her with something else. Figure out something that will get her attention, like a toy or giving you a hug or "washing dishes" on a stool at the sink, and do that to stop her from doing what she's doing. It's not teaching her any long-term lessons, but it's stopping her from doing the annoying behavior.
Also, cut yourself a break. Yelling too much is definitely something to work on, but it's not the end of the world. Two-year-olds are extremely tough customers. If you're not getting enough sleep and have other stresses, it's almost impossible not to lose it at least once or twice a day. So work on the tips above, but don't expect to stop yelling overnight, and give yourself credit for the times you stay calm and collected in the face of 2-year-old beastliness. She'll move into an easier phase soon.