I think you were really brave for putting yourself out there and asking for help. It can be so hard to admit when we are not being the parents that we want to be. I hate admitting it, but I have done some of the things you have described...grabbing my 2.5 year old's arm too hard, yelling at him, even cursing. Obviously, I'm not perfect, but I can tell you the things that I have found helpful.
First, I agree that you should try to find a parenting class or program. I've heard good things about Love and Logic. There is also a program called Parents as Teachers that is great. You have a parenting coach that comes and visits with you and helps you find solutions. Find out if they have that program in your area. Seeing a therapist would be helpful, too.
One of the things that works best for me is to pick my battles. It's so easy to feel that everything I want my son to do is so important and to get into power struggles. Sometimes I find myself in a power struggle and I realize that what I'm trying to get him to do (dump out his potty, finish his milk, stop kicking the bathtub) isn't really important. Yes, we want our children to listen to us, but I think at that age it's unrealistic to expect them to do everything we ask. Choose a few things that are important (no hurting others, don't play with the computer, or whatever really is important in your family/household) and focus on that. Let the things that are annoying, but not crucial, go.
Another thing is distraction. This really works when I can do it. If my son is doing something I don't want him to, I can often get him to stop by bringing his focus to something else. Often it doesn't matter what the other thing is if I use enough excitement and enthusiasm in my voice. This can be hard when you are feeling mad already. You want to yell and instead you have to make yourself sound happy and excited. You want to punish them but instead you have to bring their attention to something fun. But, when I can do it, it is so much easier. It doesn't have to be a big deal, just act excited and keep trying to get her to focus on this new thing.
Another thing is that I've realized that if I am pro-active, some battles never even happen. My son often climbs out of his high chair and we get into power struggles over him getting back in. But, if I buckle him in, then he can't climb out and then we don't need to fight about him getting back in. He plays with my laptop when I leave it on the couch and then I get mad. But, if I leave my laptop on the desk, where it belongs, we don't have to fight over him playing with it. It's hard to get him to wash his hands after he eats. But, if I remember to bring a wet washcloth to the table and wipe him down before he gets up, we don't have to fight about it. If I take the time and energy to enforce our rule about only eating at the table, we don't have to fight over him carrying his snack around and getting crumbs all over. This sounds like it might be helpful to you since you said you live in a small apartment and have a lot of stuff. You might reduce problems if you are able to get rid of some stuff or put things that she gets into out of sight or reach.
Finally, it's so important for you and your husband to be on the same page when it comes to rules, consequences, discipline and parenting in general. You can't expect your daughter to know what the rules are and to follow them if she gets different messages from each of you. Maybe you could share the message you posted and the responses yu got with him, so that he knows how serious this is.
I have a four month old, too, and I've gotten mad at my older son so much more since our second was born. You are just stretched thin and trying to balance a lot. With one child, if they make a loud noise, it's annoying. With two, if the older one makes the same noise, it maybe wakes up the baby, which creates more work for you and maybe causes you to lose the one hour in the day you had to get things done. Our older son was really a nightmare after our youngest was born, but it had gotten better. I've noticed that the bad behavior flares up when there's a change. For example, he started acting out again when the baby started going to daycare with him.
Good luck to you.