but you may not win. the matter of fact is your car slipped in heavy rain and caused the other car to hit you, if your car hadn’t slipped, then there wouldn't be any accident, it is your fault.
now you got sued, of course. your personnel liability limit is too low, you bought a car insurance not legal representation from AAA, their job is to pay whatever amount you've insured (15K) and get over with it. Anything additional is your personal liability, that is why the other side is suing you for. I’m pretty sure other side did some DD on you, otherwise they wouldn’t sue you for 140K, I guess. You can argue the police report is wrong, police is wrong, other side is wrong, weather is wrong, car is wrong and you’ve done nothing wrong, the problem is I don’t believe judge would take your words over police report. It is no time here to ask for sympathy but to seek a practical way to resolve this issue.
Now, you mentioned the other side is trying to settle the case, how much are they asking for? If the amount still beyond what you believe is reasonable, then you have to seek legal counsel and resolve this in court of law. I don’t think anyone here could provide any meaningful suggestion to you.