Your life gets geometrically worse the more you travel for business. The truth is that you often end up eating a bad hamburger after a long day of travel--that's if you're lucky enough to find room service open after 11 p.m. A child would only be an unwanted distraction.
Who gets to decide what an 'extraordinary circumstance' is? The airline. If airline says no, then what rights do you have? You have to take them to court.