How to add points on a spline without breaking?

In my game, a train moves along a spline and the path is very long. If you often put dots on the spline, the train behaves well, but if there are few dots, the train begins to behave strangely.

How can I add points to the spline so that they do not change my route? See screenshots.

Here you can see my route:

And here, when adding a spline point, my route collapses. How to add spline points without changing the direction of the spline?