I would like to change your thinking here. Rather than thinking in terms of eliminating the wedge turn and replacing it with a parallel turn look at teaching a movement pattern that will have a parallel relationship of the skis as an outcome. For students at this level the two main points I focus on are releasing of the old outside ski to move in the new direction and pointing (guiding) the new inside ski in the direction that they want to go.
I usually teach the release move first because it is very easy to demo to the student and easy for then to perform. From the wedge stance show them how they can make one ski or the other flatter to the snow than the other. Now add forward motion to this. As the students move down the hill in a wedge have them flatten one ski. They will move in that direction and when they flatten the other ski they will move in that direction. For many of the students you will see the first matching take place just in this exercise. Some students will accomplish the flattening with a gross movement of the body toward the ski they want to make flatten and the outcome may not be as smooth a direction change and a matching of the skis. For these students work on demoing how they can flatten the ski just using the foot and leg. As they get more skillful at this fine motor movement pattern results will follow. Those who struggle with this will be the ones who were in the widest wedge stance and those who learned to push on the skis to control speed and change direction. Point out that when they flatten one ski they feel themselves standing/riding on the other ski.
Now introduce the idea of pointing the right ski right when going right and the left ski left when going left. This is much harder to demo because it is a very subtle move and the outcome it produces, the left ski following the right pointing and the right ski following the left pointing make it almost impossible for an untrained eye to see. Because of this I use what I call a hand demo. Holding my hands in a wedge relationship I show the right hand pointing right and the left hand following it then the left hand pointing left and the right hand following it have your students do this and ask them to imagine their feet doing the same thing as their hands. Now add motion. Moving forward on the skis in the wedge stance have them flatten then point (guide) the left ski to go left and the right ski to go right. For most students this will result in a parallel turn with a wedge entry or a full parallel turn.
Considering that you are working with children you may be able to accomplish parallel turns by simply telling them to point their toes where they want to go and refining this to 'right toes point right go right, left toes point left go left'.
As to the hockey stop. Once the student can do a side slip teach them to do a quick point up the hill with one foot or the other. This quick point up the hill will bring the skis around into a braking side slip. Try to avoid teaching pushing on the skis to stop. This leads to a heel push and will carry over into their turns. Later, after the students can do parallel stops by pointing uphill, you can teach them that to spray snow they push their heels. Point uphill to stop, push the heels to spray (and stop).
Notice that at no point in all this did I tell the students to ski parallel or do a hockey stop. I taught movements that resulted in a parallel relationship of the ski and was then able to praise the students for this new accomplishment. Nor did I have to struggle with changing an old ingrained movement pattern (pushing on the skis to wedge) in bits and pieces, the old make pizza, make french fries approach. I introduced a new movement pattern that had nothing to do with the old one, was easy for the student to understand and perform and gave me the result I desired. Further, this movement pattern leads directly to the moves I will want to teach as the student progresses to higher levels of skiing.
Hope this helps,