I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
A person who stops at a stop sign is required to look both ways before proceeding (because there could be a pedestrian crossing or a disabled vehicle directly in your path, and accidents can happen). The disobeyed stop sign ticket, sounds wrong, but when you look at the statute, it makes sense. What the law says is "After having stopped, the driver shall yield the right-of-way to any vehicle which has entered the intersection from another roadway or which is approaching so closely on the roadway as to constitute an immediate hazard during the time when the driver is moving across or within the intersection, but said driver having so yielded may proceed at such time as a safe interval occurs." 625 ILCS 5/11-904. The fact that you hit the other car suggests that he was close enough to present an immediate hazard and that you should have waited. So, the ticket unfortunately is correct. You're not "responsible" for the other drive, but you have an obligation to wait for the danger to pass before proceeding through the intersection.
Now, in a normal intersection, there's no way that a car making an appropriate left turn into a side street is going to collide with a car making an appropriate right turn FROM that side street. So it does sound as if the other drive must have been driving on the wrong side of the road or otherwise making an unsafe turn such that he is at least partially responsible for causing the accident. There's a good chance the insurance companies will split liability 50/50, but if they don't, you have the ability to sue the other driver for the cost of fixing your car.
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