The 2002 Toyota Camry has had owner reports of battery problems (poor charging, frequent replacements) but if the problems you are experiencing only started after the installation of the IID, you are probably right that it is the IID or the installation of it that is the source of your car's woes.
When you take your vehicle in, ask the technicians to take a test drive with you so they can see for themselves what is happening. Perhaps if they better understand the problem, they can fix it.
It is possible he might be held liable or share in liability should an accident occur.
But he has been assured after vehicle inspections that there is nothing wrong with the IID and its installation.
If an accident occurs due to a defect in the part installed, a product liability claim can shift fault to the manufacturer. If an accident occurs due to faulty installation of a part, installation error shifts fault to the installer.
I agree that driving a vehicle with known safety issues is not smart and could wind up being a costly (and dangerous) mistake.