I'm bringing my fiance and stepdaughter here next month from Dominican Republic on a K1. Should I expect any delays at the airport coming through immigration and customs?
When you go through CBP, Customs and Border Protection, and you come through the port of entry, one of the officers are going to call the alien beneficiary, that's the foreign fiance, and the stepdaughter, into a room. There, they'll interview them and collect their documents. Your fiance will be carrying a package including the petition, a medical exam, their passport, etc. The whole process usually takes a couple hours because there's other folks that are being inspected as well. In addition to all this, you'll need to go through security, which can add another 45 minutes or so.
Because of these delays, you should not plan a tight connecting flight. Try to give yourself at least a couple of hours. In fact, perhaps 4 or 5 hours is even more safe, to account for delayed flights.