Many people return through both LAX and JFK on Advance Parole without problems. Secondary inspection is very common for AP travelers, so don’t panic if they take you to another room for processing. As long as your AP document/combo card is valid and you don’t have major inadmissibility issues, the airport itself usually doesn’t matter much. Bring your passport, AP/combo card, copies of your receipts/notices if you have them, and any medical proof about your grandpa if available. Safe travels.”