COREtec - what kind of glue for this situation?

Hi All...I put a COREtec floor in my kitchen - fantastic look and feel. Just one problem:

I have a stairway that goes down from my kitchen to a small family room. I brought the coretec to the edge of the steps.

Forgive me, but I don't know the official name for these parts - but I have a piece of coretec that is designed to wrap around that top step. It fits perfectly, and sits on top of the piece of coretec and wraps around the wood piece at the top of the steps.

The problem is, it won't stay in. I was thinking of gluing it but I'm not sure if that's a good idea, or what kind of glue to use.

If this isn't clear I'll try and get a picture posted...thanks for your help!