Passed Runner/Missed Base

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Had this the other night - Fed rules

R1 - 1 out. BR doubles. R1 holds between 1st and 2nd to make sure the ball is not caught. When she finally does take off toward second, the BR is right behind her. R1 rounds second but fails to touch the base. BR touches second and also rounds. R1 then realizes that she did not touch and returns to touch 2nd, thus allowing BR to physically pass her between 2nd and 3rd. R1 then touches second and continues to 3rd.

At the end of playing action I call the BR out for passing a preceding runner. Coach from the defense now comes out of the dug-out and wants to appeal the runner missing second, wants me to call the runner on 3rd out as well. I explain that the runner did return and legally touch the base before going on to 3rd base.

His argument was that a runner can not return to touch a base once a following runner has already touched that base. It sounded pretty convincing, but I believe that the only time a player can't return to touch a base is when a following runner has scored. Am I right or wrong here?