Why wont my Greyhound walk with me?

My family adopted a female greyhound about 3.5 years ago and I think she is currently 5 years old. She has always been shy and fearful around other dogs but we have also seen her playful side (inside the house). We try to walk her every day and she walks well with my mum and with my dad, and also if there are 2 or more people walking then she has no problem. When I try to walk her she refuses to move. I really don't like doing it but I have to drag her a fair way, until she realises that turning around would be longer than continuing on towards home. My mum gets really annoyed with me because she thinks I am not showing my dominance to the dog, and not walking her correctly or something. She says stuff like 'you hold her on a short leash and when she stops, you say be assertive, say 'no' and keep walking', and I usually end up yelling at my mum because that totally doesn't work and nothing i say to the dog really influences her at all. I just don't know what i'm doing wrong, and how to fix it.