The prevailing winds where I'm training are almost always straight down the runway or from the left. I have no problem landing on (and staying on) centerline in either case.
However, when the crosswind is from the right, I tend to land on the centerline and then skip leftward.
I thought it was just me being inconsistent about my crosswind correction. However, during a recent lesson with wind 090, I was nailing every landing on 18, but when tower turned the airport around, I botched every landing on 36, so that seems to rule out coincidentally having a bad day every time there happens to be a right crosswind.
My CFI can't explain why I'm only having a problem with one side, much less how to fix it, and seems to be blowing it off since (now that the winds are back to normal) the problem has "gone away" again, but I'm not satisfied with that.
What could be causing this, and how do I practice for right crosswinds specifically when they are relatively rare here?