Unfortunately, when she gives birth to Abel, she barely mentions it.
Immediately we see sin at work, not only in the violence of Genesis 4 but also in the parenting. There is marked favoritism of one child over another. This will be a subplot in Genesis, and it never goes well. Favoritism begins with the murderous Cain, and it ends up with Joseph's jealous brothers tossing him into a pit.
Cain shows the desire of men to relate to God in the way he thinks is right. Cain offers his sacrifice and feels strongly that God should accept it. Notice the language in the passage. There were many words used to describe Cain's birth but only a few for Abel. But not in describing the sacrifice, few words are given to Cain and more to Abel. Cain's sacrifice is on par with Abel's birth. They were barely worth mentioning.
Cain's reaction to God's counsel is that of an ungrateful rebel. Instead of correcting his offering Cain chooses to kill his brother. Later, Cain even protests his punishment. His brother is dead, but God has made Cain's life too hard to live.
Cain ends up in Nod. Nod is the land of wandering. In only a few paragraphs, we find a man far from Eden. The man Eve thought might save the world from sin has become its most notorious sinner.
And though Eve got it wrong with Cain, God is good. Another son is born, Seth. Perhaps he will be, or at the very least bring us, the saving son.
There is a lesson in Cain about sin. It crouches at the door. It desires to overtake us. It wants control of attitude, action, and consequence. The first right of refusal is yours. Who will you obey? Will you do what you want to do or will you do what God wants you to do?
If you make the choice for sin it will make the next choice for you.