Disrespectful in Never Acceptable

Dear Mrs. McVeigh,
I have a granddaughter whom I obviously love dearly, but she seems to have a problem with being respectful to me, and her grandfather. She is a pre-teen, so it could be her age, but her twin brother does not seem to have the same issue. Whenever we are with her, she feels free to give her opinion on anything and often says very inappropriate things. When we correct her and tell her that she is being rude, she does not seem to care. The biggest challenge is that our daughter (the mother of this child) will not support us when we do try to correct our granddaughter. Do we need to butt out and mind our own business and let her continue on this path?
Old Fashioned Grandma

Dear Old Fashioned Grandma,
I applaud you for trying to help your granddaughter become a better person, and for asking for respect. You have every right to tell anyone how to speak to you – especially a child. If I had one of my children’s friend speak to me using disrespectful words or tone, I would have no problem correcting him. If your daughter will not support you when this happens, I would speak to her privately about the matter (if you have not already). Express to her how you feel, and tell her how her daughter is coming across. If you do not get results with her mom, the next time it happens I would tell your granddaughter that you love her but will not tolerate her rude behavior. I would also compliment her brother whenever he says anything good, and tell him you will take him for a reward. When he is off with you getting ice cream or shopping, your granddaughter will start evaluating her words and actions.