Hi, there. I just got back and I think it is truly random. Kids will increase your odds only to the extent there are more of you, so greater odds of someone being in the right place at the right time.
For things like the ears or the dream passes and those sorts of things, they just have a certain ride and time (for dream passes its usually pretty early so you have all day to use them) and the next X number of riders to get off or all the people in that particular waiting area or the like get whatever is being handed out.
While I have no scientific basis for this, if you want to up your odds it seemed to me that most dreams were granted early in the day and/or on some of the less travelled rides/spots (though at MGM, Tower of Terror seemed to be a good place to be
). For example, one day we got Epcot dreampasses as we were getting off Spaceship Earth, which had its usual 0 minute wait because everyone had raced off to get on Soaring or Test Track. They were just handing them out to the next however many people who got off the ride. And one day we had a late lunch at Tony's Ristorante on Main Street -- it was late and not one of the "hot" places to eat so relatively empty for Disney -- and when we got to the table it was all decorated and we had a surprise unbirthday celebration, complete with cake!
I really didn't see a lot of dream-making, and each time was caught totally off-guard when it happened. Given the number of people and number of awards, I wasn't really expecting much and was pretty excited with getting anything! I was also glad that when we got them, they were in less-populated areas because frankly, going with my sons, I was more worried that they would feel left out or upset if they saw lots of other people getting things. I would have felt bad if we were having an un-birthday celebration and another family with kids was nearby, if you know what I mean.
anyway, good luck and have fun! Hope you get a lanyard.