i use my original iPad in bed every day. No problem sitting it on my chest, and holding it from there. I do wear glasses, so maybe I hold it a bit farther back than some. I haven't had any issues with it hitting my lip.
I also find that I can turn on my side, and use the rotation lock to view it while it sits on the bed, and I hold it with my hands.
I can't imagine selling your iPad because you can't get it to work in bed. I keep mine right next to my bed, and use it there about 90% of the time...