Tips further apart than tails isn't a wedge, it is a diverging parallel, or duck foot, depending on how bad it is.
Don't worry about tip lead. Tip lead takes care of itself, and has pretty much nothing to do with parallel or not. Bump skiers can stay parallel with almost no tip lead, old school skiers can stay parallel with a ton.
A divergent parallel can happen for a few different reasons. Interestingly enough, I had this very conversation on the lift with @KevinF on the lift at Stowe last weekend. It can be a functional, conscious process where the skier is using that inside ski tip to initiate a tighter turn and diminish the radius of the turn. There are much better ways to do this, but some people will do it anyways.
The other, more common reason for a divergent ski during your turn is a balance issue. If you are not balanced at the beginning of your turn, or if you don't feel confident about your balance at the start of the turn. In order to compensate for that, your inside foot will rotate toward the center of the turn, giving you a more stable platform to compensate for the poor balance.
For the balance issue, which is more likely in this case, I'd suggest practicing one footed turns. As you are about to initiate a new turn, pick up the tail your downhill ski, the ski that will be the inside ski of the new turn. Keep the tip on the snow. This will keep your balance forward, and allow you to balance on the outside ski. Complete the turn with the outside ski, then switch feet for the turn in the other direction. By doing this, you are improving and consolidating your balance, and making it less likely that you will need to diverge at the start of your turn for balance.