I believe I understand your issue. While riding a two-wheeler, to initiate a turn, you use a technique called "counter-steering". That means to start a right hand turn, you actually turn the handlebars slightly to the left, which then causes the bike to lean to the right. It's this right-hand lean that actually causes the bike to turn right. Once the right-hand lean is initiated, you then steer the handlebars slightly straight to maintain a balance between leaning too far and not leaning enough.
On the Spyder, like on an ATV, you do not counter steer. You turn the handlebars right to turn right, & left to turn left.
At first, I found that 20 years of motorcycle muscle memory was actually working against me. I was using a counter steering technique without realizing it & immediately had the Spyder move in the opposite direction I had anticipated. That in addition to the fact that I no longer was a "part" of the bike (leaning with the bike when it leans to keep firmly planted in the saddle), but was sitting on top of the Spyder & tossed to the outside when in a turn, the whole experience was other than what I had expected. When I figured out what was going on, I made mental adjustments to my riding technique and was doing just fine.
Now, take all that and apply it to the constant minor adjustments you make while going "straight" down the road & you may understand why you have that "wandering" feeling.
Hope this helps you make the adjustment.