LLXerxes: that doesn't help a thing... It may still ruin your rep when you have active deals.
To answer the question: the fact that the other AIs take the side of your enemy has nothing to do with who starts the war. It merely has to do with the question: who is going to ask the others to join? It appears that you don't do it, but an AI civ which has something to offer (gold, gold per turn, technology, luxuries, resources) WILL. If you want to avoid the other AI to gang up on you: get MA's with the others after you declared war and don't give the enemy the chance to beat you to it.
You also mention a stained reputation due to a war declaration (they don't want to trade). This has to do with the following:
-don't declare war on a civ while you have acitive deals with them (like you paying them gold per turn for a technology). Wait until the deal is over or let them declare on you.
-don't declare war on a civ when you have troops within their territory. This is consider a ROP rape (right of passage), even if you don't have a ROP with that civ. Declare on them first and then enter their territory to attack (this can be in the same turn).
To let the AI declare the war on you, you can demand them to leave when they have troops within your territory. You can also try to plant a spy (or try to perform other espionage activities). When it fails they may declare war. Getting them to declare ar will ruin their reputation instead of yours. It doesn't always work. When you are far stronger they may not dare to declare the war and then you have to wait.