Hi K.!
This tip was passed to me from another mom, and I used it to remove a whole hallway full of hideous wallpaper.
Get a "Paper Tiger". You can find them wherever wallpaper is sold. It is a little device with what looks like studded can opener wheels on the bottom. Run this over the border every which way and it will puncture the border. Just don't push too hard. Then find an empty spray bottle. Put in a couple tablespoons of regular fabric softener, Downy works great and fill the rest with warm to hot water. Spray down the border well, allow to sit for 10-15 minutes and then peel away!
The holes you made with the paper tiger will allow the fabric softener mixture to be absorbed into the border. The paper will get softened, and be much easier to remove. Make sure to use a nice big wallpaper scraper and just work the edges and reapply as needed.
I hope this works as well for you as it did for me!
L. =)