I am a Danish citizen but born in Iran of Iranian parents but have not traveled to Iran. My children are born i Denmark and have only Danish passport and never visited Iran. We have approved our ESTA for traveling to US july 16, however, after the new rules, I am not sure whether we qualify for entry under the VWP? If our ESTAs are not revoked, does that mean that we are qualified? I can't see any reason that my children can't travel under VWP??
If I understand the new rules correctly, the important thing is not whether you currently hold an Iranian passport or not, but whether you're a citizen of Iran. Did you successfully renounce your Iranian citizenship when you acquired Danish citizenship? If not, then you're hit by the new rules and need to get a visa for yourself for the trip.
US authorities have stated that they will revoke the ESTAs for travelers they know are covered by the new rules, but even if they don't currently know you might still get into trouble if they find out later (say, when you present yourself at the airport).
If your only current nationality is Danish, and you haven't been to Iran (or one of the other targeted states) later than 2010, then you should be good to go.