Can I replace the trackpad with a retina trackpad?

Sorry no, you can't swap out the trackpad for a different type.

So lets see if we can fix your problem. As it turns out there is an adjustment you can make to fix the click depression and if that doesn't work you can replace the trackpad with a new unit.

Follow this IFIXIT guide: MacBook Pro 13" Unibody Mid 2012 Trackpad Replacement. Follow the guide all the way to Step 7 After you remove the battery jump down to Step 10 looking at the photo on the left you see a triangle area of the case that sits under the trackpad the large head screw is the adjuster turn it a half turn and test the trackpad click and then try again until you get it just be careful! You don't want to fully unscrew the screw. If you can't get the travel to work you'll need to replace the trackpad MacBook Pro 13" Unibody (Mid 2009 - Mid 2012) Trackpad - Apple P/N # 922-9063.