It seems honey that you just have to follow through and be consistent no matter how bloody murder she screams...
. I guess that her screams are so vivid as you already gave up couple of times so she knows the process - you put her there, she screams, you do nothing, she screams more and you put her in the car seat. So I would just choose a method of sleep training and be persitent.
Re car seat, is there any chance she is uncomfortable when lying flat down so she prefers a car seat? At night she might be more tired and she has no power to argue about settling.
Can you also post your routine so we check there is nothing to tweak?