I am thinking that horsenettle will be more susceptible to being killed when it is in the bloom stage.  What stage is your horsenettle in? 

Also,  with horsenettle, I think a second herbicde will help the Roundup - something like Status, Distinct, Banvel, etc,etc.   Since you are talking about cotton, you may be out of luck on this idea. 

How late in the year do you see horsenettle?  Your best bet may be to scout fields in the fall, before the horsenettle leaves turn yellow, and spray it at that time of year.  Spraying at that time, the plant will be getting ready for winter, sending nutrients from the leaves down into the roots.  Applying Roundup at THAT time of year works "with" the plant's natural cycle, not "against" the plant's natural cycle. And you should get a better kill in the process.