Arriving in India with a six-week-old child after an overnight flight taught me something about travelling with children: Problems evaporate.
Everyone was queuing for passport control — our whole flight and several others, probably close to a thousand people queuing in a very large room. One of the minders saw me carrying the baby and waved us out of the queue at once. Would we please go over to the VIP&Diplomat queue. So we did, and another minder waved us out of the queue again. No, we should not queue with the VIPs&Diplomats, we should go straight past that queue and be processed immediately. The whole thing took about a minute.
That was how the trip started and that was how the rest was, too. 10/10 would do again.
If having no problems in a place like this: http://yris.yira.org/essays/1150 is the exception, then what's the rule?