When I plug in a wired headphone in to the audiojack the sound doesn't play through the headphone but plays through the onboard speakers. I tried uninstalling and reinstalling the realtek drivers and found that the headphones worked during the uninstallation/reinstallation but as soon as I restarted the computer to complete the installation of the drivers the same issue reoccurs. What could be causing this and how do I fix it? 

Not sure. Go to the Recent Issues FAQ, XPS section, and look at XPS 9343 issue 1, and XPS 9350 & 9550 issue 2, and see if any of that helps.

Assume you are reinstalling the Dell driver dated April 20, 2017? If yes, perhaps test the driver directly from Realtek.

* Go here
* Click "High Definition Audio Codecs (Software)"
* Check "I accept to the above"
* Click Next
* Look to the right of "64bits Vista, Windows7, Windows8, Windows8.1, Windows10 Driver only (Executable file)"
* Click the Global link
* The file will want to download. Tell it where to save the file so you can find it
* Run the file. Follow the instructions and restart the system when done. Re-test the audio when done

So I've been having issues plugging my headphones into the audiojack on my xps 15 9560. I know the jack works because I can plug in my headphones *during* the installation/uninstallation of the realtek drivers and the audio will work. However after I restart the computer (after driver installs) the audio will only play through the onboard speakers.

You should be getting a popup window from Waves asking what device you plugged in.  If you aren't getting that then the drivers are not installed correctly.