Get the court to set time and date when Mom is to speak with daughter. There is no need for Mom to be texting or call you. This should be through Dad or a third party mediator. You step-daughter most likely feels abandoned by her mother (this is very sad and hurtful to all concerned, but mostly to the child). Your role is to be wife to your husband and to be kind, supportive and stable to your step-daughter. If you love her, let her know (they know anyway), but also let her know that it is not your intention to TRY to take the place of her mother (even if you are a better role model...which it sounds as if you are.
The child's mother either has never learned to drive or for some reason lost her priveledges to to drive (I suspect the latter, but would not mind if I am wrong)....In any case, if she sincerely wishes to see her daughter and be a part of her life on a regular basis, it is her obligation to step up to the plate and given the history you describe, I would not make it easy for her. She needs to earn the right and show she intends to be a good and present mother.
If she doesn't better now then let the child continue to suffer.
It is so sad when adults make bad life decisions that affect innocent children.
Thank you for being a good role model for this child.....Blessings....