Hatzlocho Rabbah. I also had an experience with them and it was not pleasant.
DO NOT give them any money. Its a lot harder to reclaim your money than a stroller which is sitting in an office. You will need to go back to the airport. If possible, bring your baby and a birth certificate with you when you go. (im assuming you flew separate from your wife and the baby wasnt with you.) A copy of the law you quoted in Hebrew will help you too.
If that doesnt work, then try the other option, start a hafgana!