Dude......stahp.
No one has said anything about your source material or motivations for your project. We just supplied some technical information based on the problem you asked about. Whatever hoops that you jump through, you are not likely to beat the results of hardware upscaling to any significant degree.
There are software\plugins that you can buy.... google away.
If you have to use a VHS source, analog processing and digital capture method will have the biggest impact on your quality. Your process for getting material off of DVDs would be crucial to final product quality as well. Copy protection could throw a wrench into those works.
If simple upscaling through Premiere's or After Effects' motion settings isn't giving you the results that you want, you could export an image sequence from Premiere or After Effects then use photoshop to batch process the stills, changing resolution and adding whatever filters that you feel enhances the look, then import the the resulting stills back into Premiere as a HD image sequence. Paste the audio from the original clip to the new HD sequence, and there you are.
Have fun.