I had the same exact routine with my first as your doing with your daughter now for bedtime...and he used to pull the same stunt as your daughter. *waking up as soon as put down...or if sound asleep, as soon as he realized he wasnt on mom/dad anymore. its very strenuous to get out of this habit. luckily, she is still pretty young. here's what i suggest: put her down right before she is asleep. where her eyes are closed but she's not snoring. Than, put her down, and of course she'll fuss, but leave her in there for 2 minutes crying. It seems like forever, but she needs to get worn out anyways, so just look at it like your helping her get to sleeep faster. (i know, its hard). than pick her up, burp her cause she prolly swallowed air from hyperventalating., than put her down again ALMOST asleep, repeat. eventually she will go to sleep. the next night, do the same thing, but a little longer crying. now, the point is not to torture yourself adn your child, its this: she needs to develop the concept of going to sleep on her own. thats why you put her down when she is almost asleep, so she is already aware that she is alone. but, not making her feel abandoned. picking her up again reminds her she's loved and not abandoned. i promise it works. this also develops into a healthy habit later of just being able to put her directly into her bed when its an approximate time (say 9:30), instead of waiting till SHE is ready to go to sleep. It worked for me on both of my children. My oldest, is now 2, and he had the same thing going on as your daughter..after i did this for maybe a couple weeks, he would just sigh when i'd put him down and then stay asleep. ironically, eventually he would arch his back letting me know he wanted to be put down and he was ready for sleep. Now he plays, reads books, etc. adn then goes to sleep on his own. my now 12 week old actually insists at around 9:30 (our scheduled bed time) to go into his bed before he'll even take his bottle for bed. crazy to me, since my first had the same issues as yours. it is hard to listen to your baby cry, but your doing her a favor by teaching her its okay to sleep by herself. a couple weeks of stress for the family is well worth the years to come of easy bedtime routines. :) good luck in whatever way you choose!
in response to sleeping in your bed/carseat. this will NOT help your child learn how to put herself to sleep. this is creating ANOTHER issue you'll have to deal with. Once your daughter is allowed to sleep with you, she'll always know its an option and you're opening a whole new can of worms. 2nd-my 12 week old has terrible reflux. falling asleep in the car seat isnt the answer here. i do agree with her on the note to always go with your instincts. no matter what anyone puts on here, including myself, you'll manage and figure it out. a mom knows her child better than anyone, and every baby is different. :) your story just sounded so familiar to me, that i wanted to tell you ALL about what i did. (i wrote a novel, sorry).