My advice: You don't have to go to every fight you're invited to.
Okay, the yelliing isn't working for you or for her so, as frustrated as you are with the situation, you need to stop. Put her in her room for "quiet time" without a lot of drama. If she sleeps, great. If she doesn't, at least she'll have down time. YOU need the break too, so decide that the yelling isn't helping her sleep or helping you calm down, so take the argument away. You cannot force her to sleep so there is no point in arguing about it. If she gets agitated being in her bed, you can get one of those little foam fold-out chairs - they have arms and look like a chair, but you can unfold the bottom cushion so it's like a little bed. My stepdaughter's kids used those all the time for watching tv, and they often fell asleep in them. They come with different cartoon characters too.
We ALL get frustrated and we all go thru periods of thinking we are terrible moms. So you are normal. Don't beat yourself up about it - just move on to a new strategy. What is your goal? That she will sleep, right? The only way that will happen is if there is some calm and quiet. It still might not happen but you can't control that part. So it's quiet time - even in preschools, some kids sleep and some don't. Those who don't still lie down on the mat with a book and don't talk to anyone. Put some quiet soothing music on for her, give her some books (not interactive toys), shut the door and leave. Do it every day no matter what she does. Do not go in for 30 minutes no matter what. Put on headphones, go sit on the porch, do whatever. In a few weeks she will get into the habit, she'll realize that you're not coming in for her, and she can either scream by herself or be quiet by herself. Make sure she knows that you are doing something quiet and that you are not doing anything fun without her.
If she falls asleep in the car, when you get home, just roll the windows down and leave her there until she wakes up. Read a book or magazine, sort your coupons, or come in the house and leave the door open - use the time and let her sleep where she is. For now, though, I'd try to keep her to a schedule in her room.