Buried in wrong plot; Can they just move her to the correct plot?

You really need to be asking the people who made the mistake or a lawyer as legal issues are involved - FYI this should not cost you anything as it was not your mistake - if they do so then just you & maybe 1 or 2 others not another ceremony

Glad to hear you got it all sorted out. What a terrible stress to have after your loss. X

Talk to cemetary officials. If correct plot in same cemetary, they should bear the cost of moving remains. Get a lawyer just in case.

Talk to Plot people, If Needed, Go to Court.

There are laws pertaining to the disposition of human remains. I don’t think they can just go ahead and do it. But even if they could, I would think somebody would have to inform you.
I’m glad you were able to figure out their “system,” though.

Got it squared away. The plot map rows are numbered 1-10, 21-30, 11-20, 31-40.
Who would ever think up that arrangement? So! She is buried in the proper space. The Space # is between 21 & 30 so it is in the 2nd row. Make sense?

How awful, I'm sorry. It seems as though actually moving the cremains should be a simple matter, but like you I don't know about the red tape involved. Whatever is needed the headache and cost to correct it should be the responsibility of those who made the mistake.