Interestingly enough, the Bible takes time to point out that Isaac followed in his father’s example – even to the point of calling his wife his sister.
And the men of the place asked about his wife. And he said, She is my sister; for he was afraid to say, She is my wife, because he thought, lest the men of the place kill me for Rebekah, because she is beautiful to behold. (Genesis 26:7 NKJV)
Isaac says the same thing about his wife as Abraham said about Sarah. Either there weren’t very good looking women in Abimelech’s land, or the judgement of the Philistines was questionable. Whatever the case, Abimelech figures it out this time around. They watch Isaac and observe that he shows affection to Rebekah. He calls Isaac out on his cover.
And Abimelech said, What is this you have done to us? One of the people might soon have lain with your wife, and you would have brought guilt on us. So Abimelech charged all his people, saying, He who touches this man or his wife shall surely be put to death. (Genesis 26:10, 11 NKJV)