When I was a child we had a playground game where we would Stomp around in twos, with linked arms crossed, and then twist around.

One of the rhymes we would chant as we stomped was...

Mary Queen of Scots
She had her head chopped off.

A teacher would get very irritated and regularly told us that in fact it was a myth, but we were not interested because you cant stomp along to "She was secretly commuted into exile"

I cant find any trace of this. Does anyone know what she was talking about?

No I am not aware of any alternative History here. This just confirms that conspiracy theorists predate the internet...

Assuming you attended school in a pre internet era Honey...