It's risky, but you could go ahead and book the 2nd ticket without her SM #, and then add it back after you've cancelled the first ticket.

Though it would still be extremely easy for DL to flag it as the same person since the name, DOB/gender info, and account used for miles purchase are all the same.

It's not a 100% guarantee that DL will find the duplicate and cancel one, but if it's literally the exact same flight, it's at least a 50/50 proposition. Would be less risky if the new booking was at least a different flight on the same day.