Question: Did Eve misquote God?

Answer: She didn't misquote God.

God's Command:
Genesis 2
15.The LORD God took the man and put him in the garden of Eden to work it and keep it.
16.And the LORD God commanded the man, saying, "You may surely eat of every tree of the garden,
17.but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die."

Eve's Quote:
Genesis 3
2.And the woman said to the serpent, "We may eat of the fruit of the trees in the garden,
3.but God said, 'You shall not eat of the fruit of the tree that is in the midst of the garden, neither shall you touch it, lest you die.'"
4.But the serpent said to the woman, "You will not surely die.
5.For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil."
6.So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate.
7.Then the eyes of both were opened, and they knew that they were naked. And they sewed fig leaves together and made themselves loincloths.

God commanded Adam not to eat of the fruit. That means he was not allowed to touch with intent to eat it either. God actually commanded that Adam may not touch it with the intent of eating it. Then comes Adam's relation of the command to Eve. He probably told her the the meaning of what God said, and possibly not God's actual words.
The command: God commanded that Adam may not eat the fruit.
following that, is the meaning of the command.
Meaning: You may not take and eat it.
Wait a minute, God didn't command Adam that he may not take the fruit, only that he may not eat it.
Yes he did. God's command INCLUDED taking it. How can you eat a fruit without taking it first? The exact same thing with the word "touch". God's command INCLUDED touching it with intent to eat of it.
God commanded Adam not to touch or eat of the fruit. God didn't say the word touch, but it was a part of the actual command. This is not an interpretation of the command, this IS the command.

Yes, Adam SHOULD have stopped her. Yes, he SHOULD have spoken up. But he didn't.
This was where his sin started.
The fall happened within the course of a few minutes. There is no way that they could have refuted what the serpent said. They didn't know the difference between good and evil, they had no idea that what the serpent was saying was evil. They would have blindly accepted anything anyone said. The only thing they knew for certain is that they were not allowed to eat the fruit. Their sin was disobeying God's command. The serpent never told them that God hadn't commanded them not to eat of the fruit. He stated that had God lied to them and was only keeping the fruit from them so that they wouldn't become equal to him, knowing the difference between good and evil. . Eve's and then Adam's sin was in disobeying God's simple command. Don't eat it.
Adam and Eve's sin started with Adam's silence and continued with him eating the fruit, leading to God's curse and subsequent promise.