It's possible you are just flairing too soon. 2ft up is awfully high to start a flair with a trainer.

Let the plane come almost all the way to the ground, and flair just above touchdown, like 6inches or so. Then try to hold the plane off the ground, and it will settle right in.

If you flair too soon, you could drop the nose and bounce.

As a side note, you never want the nose wheel to touch down before the mains. You either want the mains to touch just before the nosewheel, or you want them all to touch at the same time. If you can't raise the nose to make this happen, then you're too slow. If you raise the nose and the plane climbs, you're too fast.