K.K.
First of all, for your daughter's safety AND so you do not get a ticket (or worse your daughter taken away by CPS) in the case of being pulled over for whatever reason, turn your child so she is rearfacing. If she is too small for the infant carrier seat then put her in a convertable seat that is designed to be rear and forward facing for the age/weight switch.
Regarding your daughter's tantrum over riding in the car...I am sorry to be the bearer of bad news, but sometimes children just do not like to be in the car. For some it is the constraint of the carseat, for others it's not being able to see much of the world around them. Some just don't like not being in close contact to their parent. And finally, for some, there is no reason or all of the previous mentioned.
The fact of the matter is that there are times they need to be in a vehicle whether it's for a few moments or several hours.
I, myself have a daughter who did the same exact thing you are desribing. There was nothing that stemmed her screaming and crying about being in the carseat (short of falling asleep on the longer rides) I even tried different types of seats and nothing worked.
The good news??? Your daughter WILL eventually outgrow this phase or simply stop the tantrum when she is old enough to comprehend that her tantrum is not going to do anything to resolve the situation.
I am sorry for your discomfort in the meantime. It took my daughter over a year to stop...but in that time it did lessen gradually until she only did it on long trips.
What you are doing with pulling over and giving your and her a break in the meantime is highly recommended and all you need to do is leave a bit earlier to accomplish this...Though I only suggest it if you are on trips over 15 min to/from the location, or if you get stuck in traffic..
Good Luck!!! ;-)