Take the dog on her daily walks using your trekking poles and you'll both soon become accustomed to working with leash and poles. The dog will learn to "heel" farther away from you to avoid the poles. Don't let the dog walk around you and wind you up in the leash! Teach her the "flip finish" maneuver (lots of instructional videos on youtube) so that when she's in front of you and you want her to move to the "heel" position, she won't go around you to do so.
Oh, and be sure to put rubber caps on your trekking poles during the daily walks so you don't damage the dog or your neighbors' sidewalks or the points of the poles!
As a plus, the poles turn exercise walking into a whole body exercise, using your core muscles!
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey