If I change the direction horizontally the pinned object is not flipped.
What's the deal?
I am not sure I understand your issue as the link you posted doesn't work, but you can try Pin+ addon:
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The object I pinned changed slightly its position on the Y axis once the parent object changed direction. But then I found out the reason: the origin point of the parent object wasn't exactly on the center of its Y axis. Now the problem is solved.