I am very sorry to learn about this situation.
Unfortunately, you have a very complex set of questions here, and while it may not be exactly what you were hoping for, I will try to provide you with some information to help you work through both the legal issues you raise, as well as the practical mechanism to resolve the situation.
Assuming that the brake problem was a design flaw/engineering issue (something that was caused by the manufacturer at the time the car was built), your claim at this time would be denied on the statute of limitations/doctrine of latches/and related doctrines (you had actual notice 5 years ago of a lawsuit regarding brake issues, and you did not participate in the cause of action - your basis or reasoning for not doing so is irrelevant, the key is whether or not you had notice).
Assuming that the brake problem was due to maintenance that was performed on the vehicle (you say that the brakes were worked on just prior to the accident), you would need an expert to investigate the brake system and determine whether or not the cause of the brake failure was due to improper maintenance (I did read that you said the brakes were examined, but I do not know if this was by an independent shop or by the same shop that did your brake repair in the first place). In order to pursue a breach of contract/negligence action against your dealer/mechanic you would require an expert witness that is able to testify regarding the exact mechanical failure that was at issue and the likely causation (i.e. the mechanic failed to do something, the brakes installed where below OEM standards, etc. - something was below standard of care).
As a practical matter, your auto insurance is going to be the one that is going to defend this action for you. Unless you are paying for the bare minimum coverage required by the DMV (statute), your insurance should cover both your "defense" (cost of hiring an attorney to represent you if the matter goes to court), and "indemnity" (paying any losses up to the limits of your policy - most carriers will pay even more if it will settle the claim).
Coverage for the loss to your vehicle will be set by the limits on your policy.
Hopefully your carrier is doing both of these for you, if they are not, you will want to follow up with them (in writing) and find out what is causing the problem with your coverage. If they are failing to cover you to the full extent of your policy, you can file a complaint with the California Department of Insurance (http://www.insurance.ca.gov/01-consumers/120-company/03-concmplt/).
If all that you want is to prove that it wasn't you (your carrier is defending the action, paying out for the other car, and compensating you for the loss to your vehicle as agreed), you will need to expect to pay out of pocket for an auto accident reconstruction expert with an engineering background (be very careful when you start getting into these experts - there are a great deal of different kinds of experts, some that evaluate speed, intersections, road conditions, etc. others that look at types of impact as they relate to personal injuries, and others that specialize in actual engineering causes (i.e. mechanical or structural issues with the vehicle leading to an accident - this last kind is the one you want). This is not cheap, so do consider how much you are willing to pay, and be aware that even if it is discovered that you were pressing on the brake, unless you can prove it was a fault of your mechanic (see above) you are unlikely to recover any of these costs.