Issue triangulating a font glyph for a specific scenario
The points and control points define a spline curve. Your graphics hardware is usually not capable of handling splines directly, so you convert the spline into a polygon. You'll add enough points to the polygon so that the difference between spline and polygon is negligible. Control points are NOT part of the spline! So adding them to your straight line segments is a massive mistake. Don't do that, and your problem goes away.
I'd start with the points that are given to be on the curve, then figure out how many points you need to add between these points to keep the error low enough. You might want to add points just in the middle, so the same letter at a bigger size will contain all the points of a smaller size letter plus additional ones, and the curves will look the same.
For best quality, make sure that the area where the polygon is to the left of the spline and the area where it is to the right is about the same. That's because this could affect line thickness, and that is something very, very easy to spot by the naked eye.