I've used my Diva Cup for about 4 years now. I'm on my second one. I LOVE it. They have a larger size for women who have had kids, but regardless, I suggest that you look into Kegal exercises to strengthen your pelvic floor muscles.
It will ABSOLUTELY stay in. There's a combination of the shape of the cup and some gentle suction going on, so it doesn't go anywhere. My uterus is tilted too, and I have no problems.
As for changing it, I just dump it in the toilet and wipe it out with a bit of TP. It's not bad at all, because once you have gotten the hang of inserting it properly, you won't have a bunch of blood to handle. It's all on the inside of the cup. Dump it in the toilet (don't drop it!), wipe it out, reinsert, wipe off your fingers and then go wash your hands at the sink. Too easy.
I don't use soap on it at all. As a matter of fact, the package insert says not to. I wash it with hot water every day during my cycle (whenever I have a sink available to wash it). At the end of my cycle, I boil a kettle of water and let it set in the boiling hot water for 10 minutes or so. I've never had a problem with it at all.
ETA: Veruca, love ya lady, but there is no more "ew factor" to this than there is putting a cotton plug inside yourself to soak up blood. Honestly, I find the Diva to be FAR less "ick" than tampons or pad...and no gross trashcan full of bloody feminine products to worry about.
I save about $200 a year by using my Diva cup. Even if it were kinda "ew," I'd get over it for that kind of savings.