That was an interesting one. I ran a bunch of tests last night, and it turns out the self-intersection is pretty resistant to whatever I do in MD. Extra collision thickness, lower mesh density, pressure, all to no avail. It's just that her legs push into the folds of the skirt, which have nowhere to escape to. Decreasing the fold resistance helped because there's more freedom for the cloth to get out of the way of the legs. I imagine increasing it enough for the folds not to get between the legs would help, too, but I'm not sure I'd like the look. I'll try it out later today.

Changing the animation might also help. Keep the legs together at first until the skirt has settled a bit, then slowly pull them apart and let the folds ease in.

-- I'm not mad at you, just Westphalian.