I have had better results with Duracor on horsenettle. But, I think it is a several year process. Horsenettle has an extensive horizontal root system. You can "kill" the aboveground portion, but getting the roots is harder.
Spraying in the spring (to kill thistle and general broadleaf weeds) never seemed to have much effect on horsenettle since it appears much later. I think the residual chemical will suppress the horsenettle, but not kill it completely. Waiting later to spray gives the horsenettle time to put on enough leaves to "catch" the spray, but also in this area, the grass (fescue) may be tall at that time which shields the spray from the horsenettle. I think the best approach is wait until the horsenettle is around 4-6" tall, manage stocking rate to keep the grass grazed down low enough that the horsenettle gets a good wetting with the spray, use duracor at the labeled rate for horsenettle, use plenty of good surfactant, keep spray rate high (around 30 gallons per acre), good nozzles and pressure for atomization and uniform coverage, overlap enough that you don't leave any strips. My thought is that you need to burn it bad as soon as it is big enough to catch a good dose, use a residual herbicide to suppress it until frost and hope to eventually starve the root system. Sound hopeless? I am four years into the battle and making progress. May never win the war.
I think the residual in herbicides have more effect on germination of seed than on killing roots. Horsenettle seed is in the fruit/berries formed later in the year. Seems like it would be important to clip it down to prevent the fruit development, but as late as possible. Clipping too early might stop the action of the herbicide still in the plant tissue.
Duracor compared to GrazonNext - the residual component is the same chemical in both, but at different concentration. The "instant" chemical is different - 2,4D in Next. 2,4D does not seem to be effective on horsenettle. My next step is nuclear, but not licensed for that herbicide.