How do you do the cartwheel motion?
It helps to learn the cartwheel motion as a kind of throwing motion first.
1) Go through a complete football throwing motion (as if you were throwing 10-15 yards out.) It's fine if you stride.
2) Now, lift your left hand to the sky, as if you just tossed a ball. With that left hand up, initiate your football throwing motion again.
The key to the cartwheel motion is the left hip. As you go through the forward part of the motion, you'll notice your left hip tilts about 45 degrees and pivots around a point. This becomes more pronounced, the "deeper" you throw.
Once you "internalize" this, you can go back to your service motion and self-correct.