The good news about life insurance payments, is that your mom can typically take them out as a monthly annuity or protected account, which can often be kept out of reach of the suing party. (Unless there is a legal way to force her to make monthly payments in future).
Talking with your life insurance agent is a great starting place to learn more about this.
Next, your car insurance company has a vested interest in not paying out a full 500k, and will bring big lawyer bucks to defend it, if it makes money sense for them to do so (e.g., seems obvious that the other party only needs $300k and is trying to get more). So talk with your car insurance lawyer representing you (ok, representing their money), too. At the very least, they will tell you if a claim for liability can only be made once, with the 500k insurance covering to that limit and the excess judgement going against your mom, or if you would be pulled through the courts twice. Also, note that typically the car insurance you have will help pay for your own injuries and car damage, too.
Then you can decide if you want your own independent lawyer, once you have as many facts as possible to get for the asking.
In my region, there would be only one trial or arbitration to determine total liability, from which insurance pays up to 500k. It is rare around here for judgments to go above the insurance limits, when insurance is in place, but that is trending.
A second trial / court action is started if your mom defaults on any remaining payments, to try to get a judgement to garnish wages or money somehow, but not to reassess the amount owed. If your mom is retired, I imagine that forcing her to sell her home or remit pension / annuity (life insurance) money would be less likely.
These are all my guesses, as an observer, but NON-EXPERT, even in my own jurisdiction which is not USA. Don't take advice from random bloggers, after all, but use common sense.
And above all - my sympathies for your loss. Good for you to try to help your mom by thinking through all this.