I am in haste as I'm leaving for the weekend shortly (and will have no internet access) and no time to read responses to date...
First, the most religious person I know, and among the most ethical, is a Hindu--a polytheist.
The child is not "seen as an equal to his parents" in the sense you are using. Among us heathen, a child is an equal more in the religious sense(!)--as a person deserving of having needs met, ideas listened to, feelings and personhood respected. Perhaps similar to the way fundamentalists feel about stem cells and embryos.
"This form of parenting focuses on no authoritarian rule and conflict avoidance versus parents as the authority and conflict resolution. Since this time we have seen an increase in crime, drug and alcohol abuse, teen pregnancy, divorce, etc. "
I beg to differ. I used "authorian rule," but gently, and picked many fewer battles than those that follow the precepts of James Dobson for example. I never struck my children or even yelled at them. Worst thing I said to them was "Don't be a drag." I only disciplined them in the sense of giving them some personal choices from very early childhood (red outfit or green outfit? invite Jessie over or Nathaniel?) and once I threatened to leave a restaurant if they didn;t stop fidgeting and using "outdoor voices"--I carried through. Never happened again. My kids turned out fantastic--particularly outstanding in their compassion and rationality--DS became a science teacher and DD works on democratization and governance research in Africa. Rasing compassionate and rational children was more important to me than obedient children or children with specific beliefs identical to my own. I raised children to think for themselves--so far, so good.
We have in fact seen a decrease in crime, I think alcohol abuse is flat with the past, and both teen pregnancy and divorce have been decreasing--especially in the "blue" states and cities.
"The other side believes these morals are incorrect and each person should be able to dictate their own moral principles based on their wishes and individual situation."
First, from my perspective, "the other side" is your side

Second, atheists do have morals--they just aren't the same as yours. The Golden Rule is enough for most of us. And I think of it more as ethics than morals--such a loaded word these days.
"The real question here is for atheists:
What or where do you derive your moral principles from?
Are they subject to change based on individual circumstances? "
Golden Rule, which needs to be applied diffeently in different situations (ie, is it OK to give up one life to save others--not an easy decision, eh).
"Do you believe that there should be a moral standard that a society cannot cross?"
Not really, no. I believe in the rule of law. "Moral standard" is not a meanignful phrase to me--too easily subject to individual interpretation