Who are Mary and her mother?

Indeed!  GOD chose Adam and Noah, the family of Abraham and the family of Imran above mankind of their times. Offspring, one of the other, and GOD is All-Hearing, All-Knowing.

(Remember) when the wife of Imran said “My Lord! I have solemnly pledge to you what is in my womb to be dedicated for Your service (free from all worldly work; to serve Your Place of worship), so accept this from me. Verily, You are the All-Hearing, the All-Knowing.”   

Then when she gave birth to her {child Maryam (Mary)}, she said: “ O my Lord! I have given birth to a female child,”- and GOD knew better what she brought forth,- “And the male is not like the female, and I have named her Maryam (Mary), and I seek refuge with You (GOD) for her and her offspring from Shaitan (Satan), the outcast.”

So her Lord (GOD) accepted her with goodly acceptance. He made her grow in a good manner and put her under the care of Zakariya (Zechariah). Every time he entered to visit her, he found her supplied with sustenance. He said: “ O Maryam (Mary)! From where have you got this?” She said, “This is from GOD.” Verily, GOD provides sustenance to whom he wills, without limit. (3:33-37)

Who is GOD?

“ There is no God but He, The Ever-Living, The External Power. No slumber can seize him, nor sleep .To Him belongs all that is in the heavens and the earth. Who is there that can intercede in His presence except by his permission. He knows their future and their past, nor shall they attain any of His knowledge except as he wills. His Sovereignty Knowledge extends over the heavens and the earth, and he feels no fatigue in preserving them, and he is the Most High, The Limitless.”  (2:255)