Well like I said I'm a new owner as well. If you have some advise I'm open to hearing it. Your criticism is fine but you didn't leave any opinion on the topic at hand.
Chameleon Mike, I think you got such strong and instanct reaction was because what you are suggesting will likely kill your chameleon and a very strong response to what you were recommending was more than warranted.
What you advocated was something called "flooding" which is when an animal has no choice but to experience something that it is afraid of. It can't escape, it can only endure. When you flood an animal, they basically give up (Wavingsnail called it "breaking."). Even a lab rat--or was it dogs they used in that experiment?--on an electrical plate will just give up and not respond to the torture--they'll just lie there calmly getting tortured.
To understand a chameleon's nature you need to think about its role in the world. A chameleon is food for another animal. It has very few defense strategies. It can drop out of a tree to the ground, it can remain perfectly still or it can try to frighten the other animal away by puffing up, hissing, lunging and biting. It is a slow moving animal, so very easy for a predator to catch and kill.
A chameleon has no social life. It doesn't care for its young. It doesn't form a pair bond with its mate. It is just not a social creature. It will never love you and it will never be truly tame. It might learn to tolerate you. It might learn that good things come from you and look forward to your arrival but it will likely never truly like you because it isn't a social animal. It's brain just isn't wired that way.
So, what are you doing when you hold a chameleon you just got the day before? The animal was definitely showing you and your girls that it was afraid yet you forced your girls to continue to hold him hoping that he would just get used to it. That kind of desensitization just doesn't work to over come fears. In fact, the fear often goes away for a period of time but returns with a vengeance and is more firmly ingrained. Flooding just doesn't work.
Holding an animal against it's will is stressful. A chameleon you just received might have feared for it's life for the whole time you allowed your daughters to hold it. Think about being held by a monster in a horror movie. Think for a moment of how frightened you would be. That is likely what you did to your chameleon.
Stress is not a mood an animal (or person) feels. It is a physiological state. There is a cascade of hormones that are released and they do not instantly disappear from the blood stream and tissues when the stress if removed. One hormone is cortisol which suppresses the immune system among other things. A suppressed immune system means that the animal is not going to be very good at fighting off pathogens it meets in its daily life. So, a stressed animal is more likely to become sick. And a sick chameleon, especially a sick and stressed chameleon, is very likely to die.