To answer the original problem - now read clearly. The question is how to make the datum-curve-through-points so that it is closed and has tangency continuity. I'd suggest repeating points, 10 or 20 if they are close together, to overlap the curve and then create a second curve that is trimmed to just one lap of the first curve.
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1) Don't make the points coincident in Sketcher Intent Mangler. Change the coordinates after the feature is created, outside of Sketcher. Maybe it's possible to turn off the correct combination of automatic choices that are being made that interfere with the user intent.
1a) As an aside, this is one of the reasons I miss the old Sketcher. Intent Mangler just takes second guessing, backseat driving, control freak operations to an irritating level. I hope Intent Mangler can't create new constraints as part of regen outside of Sketcher. The UI group at PTC has a new feature. When the sketch is being worked on, an on-screen window showing all the automatic constraints is displayed with a check box to show the ones that are active and a counter next to each one to show how many of those constraints are currently used so the user can both easily toggle them on and off and see that expected constraints are used and if any unexpected constraints happen. Plus, clicking on each constraint that is used, active or not, causes the affected entities on the screen to flash. An up/down arrow allows the user to step though the constrained entities. A similar box also tracks the sketched entities so that one can step through the entities to help find those pesky open-loop causes. April Fools.
2) I tried to follow the video. Does Screencast-o-matic allow capturing from more than one app at a time? Maybe use Notepad to create instructions for each step and display them. It might also be more clear with just 3 points.