My Dumb Move

[MT 73]

Varsity softball. USA rule set
I am the BU.
Batter strikes out with one out and runner on first .
Catcher drops the ball and batter takes off for 1B
Now we have runners at first and second when the PU informs the B/R that she is out on the strikeout.
As I move towards the C position I see that R2 is walking back to first base since she thought that her advance was not legal.
"No, no", I tell her,"Go back to second, you can stay there"
Which she does.
I immediately realize my error and, between innings I confer with my partner who had wanted to call her out for running the bases in reverse.
I tell him I do not think you can do that but maybe she could have be called out for being off the base when the pitcher has the ball in the circle.
Anyway, suppose I had just kept quiet and allowed her to return to 1B?
Any violations?
Suppose the ball was dead and she attempted to return?
Should I have stoppped her?
Did she violate any rules?