I lived in US for 13 years now. No criminal background, never arrested. I live with my wife and 7 years old son.

You heard right. However, the grant of a green card in immigration court by an immigration judge is totally discretionary and not a "right'". You either have to be detained by USCIS or ICE and be placed in removal proceedings in immigration court in order for you to be able to invoke the "cancellation of removal for non-LPRS" as a defense. You will need to prove that your removal will constitute an extreme hardship to a US citizen or LPR spouse or child. Your chances of obtaining a GC this way will be directly dependent on the quality of the legal representation you choose.

To apply for cancellation of removal you must first be in removal proceedings. Since it seems that you are not I would not seek this at this time. The law States: “The Attorney General may cancel removal of, and adjust to the status of an alien lawfully admitted for permanent residence, an alien who is inadmissible or deportable from the United States if the alien - (A) has been physically present in the United States for a continuous period of not less than 10 years immediately preceding the date of such application; (B) has been a person of good moral character during such period; (C) had not been convicted of certain crimes (D) establishes that removal would result in exceptional and extremely unusual hardship to the alien’s spouse, parent, or child, who is a citizen of the United States or an alien lawfully admitted for permanent residence.” Thus, if you were in removal and applied for cancellation of removal you would need to prove that your son would suffer exceptional and extremely unusual hardship. This standard is a difficult standard the generally requires some type of medical condition or learning disability. The legal information above is for general information only and should not be relied, nor does it establish an attorney client relationship. You should always consult an attorney.

Cancellation of Removal for Certain Non-Lawful Permanent Residents is a form of relief from removal (deportation) that does result in a green card. However, you have to be in removal proceedings before you can apply for this relief. Generally to be eligible for this form of relief, you must establish that you have been continuously present in the United States for the last 10 years, and have good moral character during that time, you have no disqualifying criminal convcitions, you have qualifying relatives (USC/LPR parents, spouse and/or children), and that those relatives would suffer "exceptional and extremely unusual hardship" if you were removed from the U.S. From your facts, you may be eligible for this form of relief, however, you may not be able to show the necessary hardship to your relatives. If you are currently not on the radar of Immigration and Customs Enforcement (ICE), it may not be wise to "be arrested by immigration" hoping that they will put you in removal proceedings simply to apply for this form of relief. There is always a good chance your relief will be denied, you will not receive your green card and you will be ordered removed from the U.S. This form of relief is designed to be defensive in nature, and not something you can apply for without facing removal/deportation.