Sibling rivalry. Help?

We have two daughters. One just turned 2 in April and the other just turned 4 in May. Y’all, these girls are at each other from the moment eye lids open to the moment eye lids shut. I try SO hard to get them to play nicely with each other. Our four year old is very jealous about everything that is usually the reasoning behind most fights. I got to the point for a while where I bought two of everything. That ended up being a huge waste of money because they would still fight over one. Every time they start bickering, I split them up and I talk to them about it. I feel like it goes in one ear and out of the other. Anytime I correct our four year old she tells me “no”. And I stop her and tell her she can’t tell me that, she will just shake her head no. So I’ll send her to time out and tell her to calm down and we can talk about this in a few minutes because at this point she’s starting yo get worked up. Then after I tell her to go sit in time out she really gets mad and either tells me no repeatedly or screams and runs to time out and she will scream as loud and she can like someone is hurting her. I feel like our two year old is observing her act like that and is slowly starting to pick up on it. Our four year old will typically almost always be the one to cause a fight. She takes things from her sister, will push her, tease her. Then her sister is mad so she starts screaming like a velociraptor😅 and it feels like my ear drums are gonna bleed. I also have tell our four year old to do something probably at least 5 times before she even makes an attempt to do it. For example, I’ll ask her to pick her toys up after she dumps the bucket out and she says she can’t, it’s too heavy. So I told her, “Sister and I will help you but I need you to pick this mess up, it was just sister who made this mess” and then she will just stare at me. So I’ll ask again, and she will kinda get fussy. Then again and still nothing. I’ll get to where I say “fine, you will have to sit in time out if you’re not going to help” and like stated above, she then looses it.

I didn’t have a great role model growing up. My step father was extremely physically abusive and also sexually and mentally abusive for almost ten years of my childhood. I’ve went to therapy for it but I still suffer with PTSD and anxiety from my childhood. I don’t really know what to go off of. I just know that I don’t ever want our children to look back on their childhood and never feel like they where loved like I did. I always stick to trying to talk it out with them. I’ve read article after article and I feel like nothing helps at all. I feel like her attitude is getting worse, she will talk back to me several times a day, tells me no or says I don’t want or I’m not doing it. She is in pre-school and her teachers say she is absolutely wonderful. She’s incredibly smart and very sweet and they never gave to ask her to do anything twice.

Is it normally for them to fight almost every waking second of the day? Or four our four year old to be so defiant? I feel like I’m doing something wrong and it just eats at me and I feel like such an awful mother.