The icing curdled when I was whipping it! Everything looked good until I added the cornstarch/ powdered sugar mixture. Any advice?

It sounds like you may have overwhipped the cream, or your mixture wasn't quite as cold as it needed to be. That allowed the fat in the coconut cream separate out. Chill your mixture really well, and then try gently beating in a few tablespoons of heavy cream. I recommend whipping at lowest speed, or by hand. You just want to take it easy, so you don't end up with butter.

Hmmm.... was the cream/cornstarch mixture cooled? I have never had that happen to me. Did it separate? Once you have partially whipped the cream and add the cornstarch mixture it should thicken when you continue whipping. Maybe put the cream in the refrigerator and get it cold then try whipping again. Please let me know how it goes: