Is the Hajj performed by the questioner and her mother valid, and is anything required of her due to her not stoning the Jimar on the eleventh and twelfth days of Dhul-Hijjah, and is that Hajj considered Hajj Al-Islam?

You erred by not performing the stoning (ramy) on behalf of yourself and your mother, and you must seek forgiveness and repent. Your Hajj is valid, but each of you is required to offer a sacrifice (dam) to be slaughtered in Mecca and distributed among the poor of the Haram (definition), due to abandoning the stoning, which is obligatory. Inform your mother to make the intention, when offering the sacrifice, that it is to compensate for abandoning an obligation. Your Hajj counts as Hajj al-Islam if you were an adult (completed fifteen years of age) at that time.