Nice sentiment (how could it not be with a subject like that?) To me it seems a little bland because of the cliches like climbing a mountain and touching the sky, city lights, followed her dreams. They're all also a bit vague. This could be anyone. There's nothing that tells us why your mom was special. I can't really help because I didn't know her, but I have a feeling you would be better to add detail and color - where did she move to, what did she feel on leaving. You hint at something bad in the past and in the future -

She ran for her life

Never knowing what was to come

- but we know nothing about what these were. Help us to know her and feel with her.

How about:

She’s still the little girl inside

That ran down the sandy road

That led to her grandpa’s farm

Dreaming of the city lights

She ran to where the blacktop begins,

to find a new life

Spread your wings and fly away tonight

Spread your wings and fly away

She says she'll go to Dallas

A good job is waiting  for her there

her mom says" Its too far."

 Shreveport's a better town

and the Hayrides there