Re: 4 week old will only sleep on me!
If she's your first/only, I'd just hold her. I could not put my first son down at all for naps. I read a lot of issues of The New Yorker that had been piling up, but didn't get much housework or cooking done. He also did not really like to be swaddled, but we did end up letting him sleep on his belly from around 7 weeks on. Like you we were worried, but ridiculously sleep deprived. He did somewhat better with that. Also, if she takes a nap, you should take a nap. I kept doing that even after my son was sleeping through the night. So, yeah, it was held during the day, sleeping on his belly in our bed at night. It worked out fine, and he was a difficult sleeper for a while, but around the time he turned 1, he became an awesome sleeper, and still sleeps like a champ at 2 years old. Basically, it is a season of life that will magically become a distant memory soon.
My second son is a swing addict since I don't have the ability to always hold him and play with the two year old. The swing is the only place he will sleep for much of a stretch. On a rough night, he'll even spend a few hours in the swing. Ours does not plug in and we're going through D batteries like crazy! I don't think it is messing him up - I can't see how it is any worse than laying on his back in a crib?
SAHM to B (10/10) and E (9/12)