Random assignment of treatments to half of a group

I am in the process in randomly assigning treatments for an experiment. I have four sites (Site1, ... Site4) where 12 experimental units (e.g., 1 ... 12) are replicated four times (e.g., 1 ... 4). For each replicate, I have randomly assigned one of three treatments (e.g., trt1 ...trt3).

I now need to assign a SecondTreatment (y or no) to each Treatment within a Replicate for each of my Sites. trt2 should always be "y", whereas I want to randomly assign "y" to half of trt1, and "n" to the second half of trt1, and then do the same for trt3. The should give me for each Replicate: trt2 with 4 "y", trt1 with 2 "n", and trt3 with 3 "n".

My data looks like this:

Site      Experimental unit     Replicate   Treatment        SecondTreatmentAssign (y/n)
Site1              1                1         trt1  
Site1              2                1         trt2  
Site1              3                1         trt3  
Site1              4                1         trt3  
Site1              5                1         trt1  
Site1              6                1         trt2  
Site1              7                1         trt3  
Site1              8                1         trt2  
Site1              9                1         trt1  
Site1              10               1         trt1  
Site1              11               1         trt3  
Site1              12               1         trt2  
Site1              1                2         trt2  
Site1              2                2         trt3  
Site1              3                2         trt1  
Site1              4                2         trt2  
Site1              5                2         trt1  
Site1              6                2         trt3  
Site1              7                2         trt2  
Site1              8                2         trt2         
Site1              9                2         trt1  
Site1              10               2         trt2  
Site1              11               2         trt1  
Site1              12               2         trt3      
Site1              1                3         trt2  
Site1              2                3         trt1  
Site1              3                3         trt3  
Site1              4                3         trt3  
Site1              5                3         trt2  
Site1              6                3         trt1  
Site1              7                3         trt3  
Site1              8                3         trt2  
Site1              9                3         trt1  
Site1              10               3         trt1  
Site1              11               3         trt3  
Site1              12               3         trt2  
Site1              1                4         trt3  
Site1              2                4         trt2  
Site1              3                4         trt1  
Site1              4                4         trt3  
Site1              5                4         trt2  
Site1              6                4         trt1  
Site1              7                4         trt3  
Site1              8                4         trt1  
Site1              9                4         trt2  
Site1              10               4         trt1  
Site1              11               4         trt2  
Site1              12               4         trt3
  .                .                .           .
  .                .                .           .
  .                .                .           .
Site4              12               4         trt1  

I'd like to be able to do this in a way that makes these assignments back into the dataframe that way I don't have to manually move anything around. I am still quite the novice with programming and not sure how to make this happen.

Thanks!