I personally feel that no pull leashes, harness, and collars only mask the problem instead of fixing it.
Like carmspack said, Training is the only way to actually fix the pulling. Once my girl learned to heel she didn't pull, but I still don't walk her on just a flat collar. I can and she does fine but Prong Collars allow you to have that training tool to correct when needed.
The others are also right when saying correcting at the wrong time or on accident can cause further problems but honestly I feel just for walking it would be fine for your parents to walk her on a prong collar after she's been trained as long as you educate them on it a bit. i.e. Don't yank it about or make sudden movements.
Once she's learned to walk properly or heel then if she pulls, just the pressure of the prongs will more than likely put her back into place and a light snap of the collar will let her know that she's out of line.
Because my dog was taught to Heel all I have to say is "Heel" when she began to go ahead of me and she falls back into place. If she doesnt I say "Heel" again and snapped the collar lightly and that usually gets her attention.
Also just so you're not confused this is casual heeling not competitive. It just means the dog walks at your left, with their shoulder at your leg (how you probably want her to walk) They can look around, have a loose leash and be a doggo but also will look to you to know when its okay to go off and sniff, go ahead, or fall behind. My dog also sits when I stand still which I find extremely helpful since she's still young and full of energy.