I have been using a Diva Cup for years, and I madly love it. It's a serious money-saver, and it's so bleeping convenient to pop it in place in the morning and not think about it again until I get the kids home from school. I hate using pads. I think they're kind of icky, to be honest. And before I bought my cup, I was fearful it would be, too, but it's actually much neater than using a tampon.
I've had no issues emptying it away from home, when necessary. I keep a small pack of wet wipes in my purse (plastic snap bag with about 5 wipes), dump the contents of the cup in the toilet, wipe the outside, if necessary (it seldom is) and put the cup back in place. Of course, I clean the cup out once I get home, but if I'm flowing heavier than usual and need to change the cup, well, you do what you've got to do.
Motherhood: When changing from pj pants to yoga pants qualifies as 'getting dressed'.