My ds is just 5 months old and was/is the SAME WAY. Hates his carseat!!! It has brought me to tears on many days and I've had to rearrange my expectations more than once and keep reminding myself to slow down, stop trying to do too many things, etc. Then there are the days when I absolutely HAVE to get out. Things that helped me:
1) nursing, nursing, nursing babe before going out. Make baby as fat and happy as possible.
: Sometimes he would fall asleep. If it was after a good nap he could then "play" with things.
2) There was a HUGE leap during week 12 when he could finally see his mirror in front of him and feel this little zebra stuffed musical toy at his barefeet, and had something to hang onto (for him it was the carseat belt...we were travelling that week and didn't have the base with us).
3) Plan only ONE car trip a day. I lowered my needs/expectations for getting out and this helped lower my frustrations. My husband is awesome and does the grocery shopping on his way home from work.
4) go out and walk as much as possible...my son LOVES to be outside now and its healthy for me, too! If I could rearrange my life I would move somewhere where I could walk to a lot of things (parks, walking trails, stores, etc.) As it is now I've not got nice places to walk to, but I do with what I've got and at least I get out.
5) invite people over to YOUR house for social time
6) Have someone else drive so you can be in the backseat with babe
7) When we went on 3 long car trips trips in 1 month I thought I was going to lose it. I resorted to giving a bottle of expressed breastmilk to him while he was in the seat and then formula when I couldn't pump enough to keep up with him. It's a comfort thing and allowed him to calm down while being in the carseat and he would often fall asleep. I did this when stopping to feed wasn't working anymore. I'm sure others wouldn't recommend this---but it saved my sanity.
8)opening the window a little can help...white noise and fresh air
9) and always remember my new acronym: NIPL (nursing in the parking lot). give yourself much more time than you think you'll need for each outting. Don't be resistant to stopping and feeding babe in parking lots. I find parking lots that make me laugh to nurse in now...church lots, funny restaurants. Just think of all the stories I'll be able to tell him!
10) find the shortest routes, fewest stoplights and sometimes you just go and apologize and kiss them a lot when you get home.....
IT WILL GET BETTER!!! Be patient...I really hope you don't give up breasfeeding?! Good luck