What type of border?
 

Any suggestion on what type of border (not flowers or groundcover) we can put between the rocks and mulch?

We don't want something that needs to be cut and thus sloppy looking.

thank you!

I would just remove the mulch and fill the area with more rock. The stones are very nice and would be a better border. Maybe put some mulch in front of the stones in a little bit of a ditch.

No-dig is the only border I would use. Get it from Southern Landscape supply. Is a commercial product. Easy to use and outlasts metal edging. (is PVC, not plastic)