Applying to register as a permanent resident to be with my American wife and son.

Yes. Your admission on visa waiver after marriage to a US Citizen is problematic to an application for adjustment of status. Please consult with an immigration attorney to discuss this case confidentially.

Hire an immigration attorney. You WILL encounter difficulties. Whether you would be able to adjust depends on the circumstances of the case and cannot really be predicted on . Whether you would encounter difficulties is an easier question - you will. WHy? because under the ESTA, as you know, you are only allowed to stay for up to three months and must have genuinely nonimmigrant intentions. It is hard to believe, though I am not saying that it is impossible, that you had not known about your intention to seek residency based on marriage before you came to the USA. If I was that immigration officer, who would be adjudicating your petition, I would have hard time believing that. Hence, you need to run your case by an experienced immigration attorney before you do ANYTHING. It is in your best interest and that of your family.

It will be very difficult for you to apply for a green card based on the fact that you entered on an ESTA visa which requires you to leave after 90 days. Consult an immigration attorney.

Be careful with the pre-conceived intent issue. Please seek the help of an immigration lawyer who can guide you with the right course of action.