We are currently having problems with our current bonding method. We bond the Unplasticed PVC to ABS and then cut a chanel out of our PVC, effectively turning it into two separate pieces both bonded to the ABS.

However the bond isn't strong enough and when we cut the PVC it is moving and eventually becoming unbonded.

What is the best/strongest way to bond these two substances?

Have you considered a nonadhesive bond? Like a pressure bond like some sort of clamping or binding.

Anyway...
WO-1802 Acrylic Adhesive
WO-1007 Vinyl Adhesive
SC-325 Polycarbonate Adhesive

http://www.rplastics.com/weldon1802.html

http://www.eplastics.com/Plastic/ABS-Glue