Because the second marriage is bigamous, it's null and void; they were never really married, and as such his "second" wife and kids can't be sponsored for a Green Card.
I don't know if bigamy would affect his own Green Card status, but it's certainly possible! It's a very bad idea, in any case.
Part of the petition for an alien relative is submitting documents. When the U.S. citizen files the I-130, which is step 1, then he will need to prove the family relationship between himself and his wife. For that he will have to submit the Certificate of Marriage.
At the consular stage, the same Certificate has to be submitted. At that time they need to see the divorce decree from his first wife. They know about his first wife as that's how he got his Green Card in the first place. So if the date of his divorce from his first wife is later than the marriage to the 2nd wife, then the second marriage is void, the reason for the petition does not exist, and the petitioner will be prosecuted for polygamy indeed.
If the naturalization of the US citizen lies less than 2 years back at that time, it could also result in unwinding this without the help of a judge. At that time the "it was only a dream" not-US citizen will be ordered deported once he has served his prison sentence.