Beautiful little Piet.
I wanted to add some information here that you may or may not have. That "turbulence" you're hitting are thermals releasing. Thermals are like the bubbles in a pot of boiling water, they form at the bottom (ground) until they get big enough then release and rise. When there's enough heat in the system they just keep releasing in an almost constant stream. In the video you can see birds in the distance soaring one of those bubble streams; a larger thermal. The more heat the ground can absorb the more heat it can radiate and the faster it can generate those thermals.
Hot, dry air (like from the sun-baked dirt of a field) will generate more thermals because it will heat up faster. Wetter air like you'll get over a body of water or lush greenery will generate less lift. Sometimes you can actually get something called "tree sink" where the air above a tree line is so much cooler or wetter that it sinks, pulling your plane down towards the trees. Staying over that lush, green runway will keep you in an area of low- thermal activity because there is more moisture present and the grass absorbs a lot of that heat.
Does it wag the tail around a lot in turns? My Q-tee does that, because it doesn't have much dihedral, and subsequently is relatively slow to auto-coordinate. Especially when starting and finishing them.
I would tend to associate tail wagging with an under-sized vertical fin more than the lack of dihedral, though they do both play a part.
It would probably fly better with more dihedral. Turns can be tricky. It'll bank real hard and will dive if you aren't careful. Once it is banked be ready to give it rudder in the opposite direction or it'll continue to roll. It's sensitive to changes air movement. It'll be flying straight and level and a small gust wil roll it or knock it off in another direction. I found myself most comfortable flying it two mistakes high at low throttle.
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Now that I think about it ... it doesn't yaw a lot with the rudder. The most noticeable characteristic is the tendency to roll with the rudder, like the mini SE5 and DR1.
With a 3-channel plane like this you want some roll-coupling (where a rudder input causes the plane to roll) so that it can bank without ailerons. But, too much dihedral can get you excessive roll-coupling and make things unmanageable. It looks to me like your Piet has just about the right amount. I think a little wash-out in the wingtips would do more to improve the way it turns.
I had a similar problem with my FT Simple Soarer when I built a new wing for it. Without some washout in the wing it would take a lot of rudder before the plane started to actually turn, and about the time it did, the plane would bank suddenly and pitch the nose down. This was most-likely the wingtip stalling. Giving just a little washout helps keep the wingtip flying and makes turns much more predictable.
The fact that you also have to give immediate opposite rudder to stop the turn makes wonder if you may also have too much expo. If there is too much expo, the dead zone around center stick is too large you'll be feeding in more and more rudder waiting for something to happen, then by the time something finally does happen you've already moved the stick farther and have to jump back the other way, and you can end up fighting the corrections you just gave. This leads to pilot-induced oscillations, where you're just fighting yourself trying to find neutral. This is a personal-preference and can vary from airplane to airplane. Personally, I never fly with more than 30% expo and keep it turned off for anything but my faster/twitchier planes.