Isaiah uses the relationship between a mother and her child as a metaphor in different ways. First, he compares God to a mother, and Israel to his child:
Can a woman forget her nursing child. And have no compassion on the son of her womb? Even these may forget, but I will not forget you. (Isaiah 49:15)
He both suggests that he is like a mother, but also that his bond with his people is even more intense than that of a mother with his child.
Israel itself is also said to be like a mother attempting to give birth to a child, although that child probably represents Righteousness or, perhaps, the Messiah:
Like a woman with child, who writhes and cries out in her pangs when she is near her time, so were we because of you, O Lord. (Isaiah 26:17)
Israel's sufferings under the wrath of God are compared with labor pains, because they're going to ultimately bring forward something good: the surviving remnant of the people who will live in a time of endless peace.