A.,
It sounds like she is trying to transition to two naps. You might try putting her down a little later than her normal first nap, then down earlier than her third nap. It can take a couple weeks for kids to fully drop a nap, so I wouldn't worry about getting her to sleep in the swing/car, if that is what it takes. If you can't get her to sleep with only two naps at home, just use the swing/car for a little while. Once she is firmly on her 2 nap routine (if this is, indeed, what she needs) then try to retrain her to sleep at home.
A couple notes on sleeping in a Pack & Play. First, it is not the P&P that will give her a flat head, it is just lying on her back. A swing or carseat will do the same thing. Regardless of where she gets it from, it is completely harmless, and will go away as she spends more time off of her back. If you are really concerned about it, make sure she gets plenty of tummy time. Second, she might resist sleeping in the P&P because it is uncomfortable. Their "mattresses" are flat and hard, and she may not like it. Do you have another place you could try her naps? A crib, or a mattress that is flat on the floor?
Finally, for more specific advice, I would highly recommend "The No Cry Sleep Solution for Infants" by Elizabeth Pantley. I think the previous poster said it all about letting babies cry it out. Your baby is trying to tell you that she needs you, and at this age, she really needs a responsive mommy. She isn't trying to manipulate you, per se. She is just trying to get her needs met. If you meet them, she will be free to grow to the next stage of development, content and secure that she has what she needs. If you ignore them, she will either get more emphatic about it (ie, scream harder and longer), or she will just give up. While many moms think that their baby has "learned" once they stop crying, what they have really done is realize that there is no point expressing their need, because no one is going to meet it. On the other hand, you don't have to become a martyr, and let your baby nap on your lap every day, if that isn't what you want to do. That is where Pantley's book really helped our family. I think she finds a middle of the road solution - not leaving babies to cry unconsoled, but also helping them learn to sleep well. Hang in there, it will get better!
Best of luck,
S.