First I have to say that you should check the weight limits on the swing. Depending on what type of swing you have they could be dangerous at this age. I speak from experience. I did not know this but most swings have a 5/6lbs limit. Meaning that you cannot use until then. Our daughter was 4lbs. I always assumed they were safe to use right away. Two days after bringing our daughter home she was in the swing and stopped breathing. In the ER we learned the dangers. In young infants upright positions (as with some swings) can cause their ribs to press into their stomach causing reflux to go up the esophagus which can be choked on. We didn't use the swing again until 3 mon. It is recommended that the seat be in a "lay" position, or a cradle type swing.... ours was not, not adjustable and sat in the upright position. Anyhow, once there stomach muscles develop and are able to keep the food down it is no longer an issue. That being said I just read a book by Magda Gerber, she is against using a swing. Her premiss is that a swing is artificial, artificial movement, attention, and that far to many parents use one as a means to checkout, "babysit." I wouldn't go that far but it is an interesting read. Some babies don't like the movement, and swings are only recommended for 30 min. Ours would rarely fall asleep, she would play. You said that your daughter does like it, does sleep, but you don't want her to be dependent on it. What if you are out, without a swing. And you want her to sleep in her bed.
Try undoing the swaddle not all babies like to be tied up. Try dressing her in warmer clothes and let her to be free to kick... another Gerber/Pickler method.
Lastly, we do have friends whose three girls all refused to sleep on their backs. Their father is a general practitioner. The girls refused and knowing all the science as to SIDS they continued to let them sleep on their stomach. Not without precautions. They used the movement/heartbeat monitors. Our daughter slept on her back until she could roll over now she sleeps exclusively on her stomach.
Get her out of the swing. Try letting her sleep in the car seat, our Ped recommended this. You can rock her until she falls asleep. Does she sleep in a boppy? Many babies I know do, next to mom on the couch. This might work for naps but at night go with the bed/bassinet. Keep putting her in her bed. She has to learn to sleep there and she has to learn to self-soothe. Yes, it is hard but it will pay off in the end. You are doing yourself and your daughter a great service by teaching her to sleep in her bed.
Oh, one last thing we did with our daughter... for more than one reason. Our daughter loves her bed and will sit and play after waking up sometimes for an hour before crying out. She is very comfy in there. I read to let your child play in bed. At times when she is not expected to sleep. We all know the no toys no stuffed animals, blanket rule. However a few times during the day I would lay her in there with a few of the above to play. This is when a mobile comes in handy, we had two, I would clip on only at playtime. I would leave the lights on, even turn the radio on.... as to signify that it was not sleep time. I would stay close to comfort (only peaking in on her,) usually putting away laundry, cleaning, ect.. It gave her independent playtime, confidence and made her comfy in her bed and let her know that she could be there alone. At night remove the toys, turn lights off, ect. Night time bath, book, ect, signifies bedtime and the difference between the two but the comfort and confidence in being alone remains. It worked like a charm, one of the best thing we did. She slept in her bed at 12 weeks and from 8-8 by 16 weeks. She has no issues with her bed/room and to this day she does wonderfully playing alone and can keep herself occupied in her room for an hour.