Can't attach spinner to top arm of dishwasher

The spinner that attaches to the arm at the very top of our dishwasher fell off, with a clearly broken insert that could no longer attach it to that arm.

I ordered a new part (8193768) which came as a spinner (identical to the old one) and an insert that is more complete than our broken one, but which still won’t hold the spinner in place under any pressure at all.

The insert (which looks roughly like a cylindrical T) does not have any threads or expansion of any sort to positively attach it to the upper arm – just a loose friction fit. The part that sticks through the arm has a slotted end – a central hole with 3 slots radiating out at 120 degree angles from each other. Is something supposed to attach to that to lock the insert in place? (If so, shouldn’t that have been part of the replacement package?)

If there is no such part, would gluing the insert into the arm be a reasonable option? This is an absurd amount of work for such a tiny problem.

Any information or advice appreciated. Thanks…

(P.S. I registered, then followed a link from there back to enter a previous post, but then when I hit enter it erased everything I had written and told me I needed to log in, with no way to recover my original message. That’s an annoying bug in the interface.)

There is in fact a third part that attaches to the insert.

It was just very small and for unknown reasons came in a separate tiny package from the other two pieces. With that attached, the spinner works
perfectly…