How to create a column based on multiple criteria in r?

Currently I have a variable "Sex" that contains 1's and 2's for respectively men and women. I want to add random noise to this variable. Therefore I generated random numbers using a normal distribution. The next step is to determine if some of the values have to change to the other sex. I use a z-value of 2 and -2 as boundaries. So if a man (1) is assigned to a value >2, it has to change to a woman. It works also the other way around, so when a woman (2) is assigned to a random z-value of <-2, the sex variable has to change to man (1). In all the other options, the value has to remain the same value.

I thought a ifelse statement would do the trick. Unfortunately it did not work. My statement looks like:

with(Dataset18$New_sex,
     ifelse(Sex== 1 & Norm_dist_random > 2, 2 , ifelse(Sex== 1 & Norm_dist_random <= 2, 1, 
     ifelse(Sex== 2 & Norm_dist_random < -2, 1, ifelse(Sex== 2 & Norm_dist_random >= -2, 2))))
)

My data looks like:

Sex     Norm_dist_random
 1         0.622221897
 1         2.573726407
 1        -0.298095612
 1         0.717745305
 2        -2.597695772
 2         2.534427904
 2         0.089732903
 2        -0.329274570
 2        -1.173434147

In the end my data has to look like

Sex     Norm_dist_random   Sex_new
 1         0.622221897        1
 1         2.573726407        2
 1        -0.298095612        1
 1         0.717745305        1
 2        -2.597695772        1
 2         2.534427904        2
 2         0.089732903        2
 2        -0.329274570        2
 2        -1.173434147        2