I followed the directions exactly. But when I added the butter, it never had that curdled appearance and then became too soft. Do I have to start again?

Is it warm where you're working? Or was your butter too soft? You might try putting it in the fridge to firm up, then letting it come to room temp again and rewhipping. SMBC is a thin consistency icing to begin with I think. Have you made SMBC before to know this version is too thin?

Stick the mixer bowl in the freezer for a while, and then whip it again. Don't freeze it completely, just leave it in there long enough for the butter to harden up a little.

I am trying to chill it and re-whip. I have made it before, but I thought it was softer due to the fact that I used egg whites from a carton. This time I used real egg whites. I assume that I will have to refrigerate the cupcakes once frosted to keep this stuff from sliding off.

Yep, SMBC problems are almost always fixed with some temperature manipulation