If a child had vomited near me, and it bothered me, I would have quietly asked to be moved, and if my request wasn't met, I'd have left the restaurant, having orderd or not. And, yes, I would have stepped over the offending vomit to do so.
If I chose to stay, then I would have ignored the situation as best I could.
I would imagine that WDW CMs clean up vomit multiple times every day, so to them, it's not as big of an issue as it is to you.
I would not have made a scene or made the child feel badly. I am sure that the kid was probably embarrassed enough.
If it were my child who vomited, sick or not, I would have left the restaurant. Maybe I would have stayed at Epcot and tried to find an IllumiNations viewing spot out side somewhere, but I would have left the restaurant. It would really depend on why the child had vomited...were they sick or was it just one of those gag vomits which, while your child may not do it, a lot of children do.
As far as clean-up, I would assume there are health department rules as to how that sort of thing has to be handled, and what chemicals or cleaning agents have to be used, so smelly or not, that's life.
As others have said, if you reread your original post, it does not come off that you were "quiet or discreet". Maybe you were "expounding" a bit on the post for literary effect, but remember, on the computer, we cannot read your tone or expressions, so the written word is all we have to go by.