Vitsy, 11 9 88 6 Bytes
This programming language was obviously made past the date of release for this question, but I thought I'd post an answer so I can a) get more used to it and b) figure out what else needed to be implemented.
'rd3*l\O'rd3*Z
The explanation is as follows:
'rd3*l\O
' Start recording as a string.
(wraps around once, capturing all the items)
' Stop recording as a string. We now have everything recorded but the original ".
r Reverse the stack
b3* This equates the number 39 = 13*3 (in ASCII, ')
l Get the size of the stack
\ Repeat the next character for as many times as the top item of the stack specifies.
O Output the current item of the stack, removing it after outputting it.'rd3*Z
' Start recording as a string.
(wraps around once, capturing all the items)
' Stop recording as a string. We now have everything recorded but the original ".
r Reverse the stack
b3* This equates the number 39 = 13*3 (in ASCII, ')
Z Output the entire stack.