I don't know anything about in street split-point switch machines. Streetcar lines and many railroads used single point turnouts in the street, where only one of the two points moved at all. However normal split-point machines have basically three adjustments. The first may be on the connecting rod that holds the two points a fixed distance apart If this rod adjustment is correct, whenever one point lies against the stock rail, the other will always be the correct distance from the other stock rail (typically 6 or 6.5 inches). This is not adjusted in the switch machine, but on the connecting rod. On many switches, this is not adjustable, since it should never change. Often the clips that hold the connecting rod to the actual point has a series of three offset holes, by moving the connecting rod bolt between holes, the distance between points can be adjusted.
The second is an adjustment that determines how far the switch rod itself moves. This is usually under the switch machine and consists of a screw eye bolt that moves back and forth when the switch is thrown. The switch rod connects to the eye with a clevis. It may be possible to take off the clevis and unscrew the eyebolt. The more threads that are showing, the longer the throw. The third adjustment, which usually needs adjustment from time to time, is a fine adjustment used if one side is too hard to throw and the other doesn't pull up to the stock rail when thrown. The adjustment is underneath the cast cover on top of the machine. It should be possible to rotate or remove this cover to expose the mechanism inside The should be a number of small wedges which can be moved when the stand is halfway thrown from one side to the other to adjust the exact point where the pivoting is stopped.
Normally on a spring switch, the actual switch points are held together by a rigid bar, so the points are always the same distance apart (unless adjusted as mentioned above), and move back and forth together as a unit with no movement between the two points. The spring is between this connecting bar and the actual switch rod, which connects to the switch stand. There are usually adjustments on the switch rod at this connection to adjust spring tension and/or make fine adjustments to the throw.
It sounds like your switch points are two close together if one side makes up while the other side is too close to the stock rail. I would check that the two points are rigidly connected together, with no relative motion, and the proper distance apart first.
Peter Schmidt