The warmongering penalty for taking cities is not at all correlated to who initiated the DOW. Many people seem to find that perplexing, but it is how the game works.
Initiating a DOW is actually a pretty minor diplomatic penalty. If you are trying to make an AI look bad, see if you can get them to denounce you while you have an active DOF going. But really the player seems to be held to much higher expectations than the AI.
In terms of baiting the AI, to DOW or denounce, there are several dialog box options. Tell them not to spy on you, not to settle near you, not to spread religion. You can bully CS that they have allied or pledged to protect. Denouncing actually seems to make them less likely to DOW, and will anger their friends.