No, that children should obey there parents is not the moral of the story. The moral is to not act impulsively. If Juliet would have listened to her parents, she would not have died, but she would be unhappily married to Paris and ended up living a sad existance for the rest of her life. I don't think Shakespeare would promote the idea of young people abandoning the ability to think for themselves to blindly follow their parents. Shakespeare is cautioning kids about the danger of spontanaity and lies. The web of lies Romeo and Juliet create spreads so far and wide they can no longer navigate it and ultimately find themselves at a loss for which direction to turn and end up dead. If anything, a moral could be directed at parents to give their children more freedom to make decisions for themselves and to be more open and communicative with their children in order to foster a more understanding relationship.
There might be many meanings in the drama. I think it's safe to say that one of them is not that children should blindly obey their parents. Shakespeare does a fairly good job of representing how wrong the parents are in this configuration. Evidence of this can be found in how the Capulets treat Juliet in their demand that she marry Paris. It does not represent the best in parenting when the mother says that she is "done" with her daughter and when her father pretty much disowns her, indicating that he doesn't care if she begs in the street. The entire premise of the feud, itself, is never clearly distilled, indicating that the parents are fighting a battle whose cause is not known. In this light, I think that Shakespeare is suggesting that the parents might have set themselves on the wrong path and that the children might have been ahead of the curven in trying to set things right. The reconciliation at the end of the drama is indication of this, and proof that the kids might have been right on this one. The children represent the example for the parents.