This is one of those unfortunate circumstances where you can sue, get a judgment for a larger amount than the policy limits but be limited in what you can collect because you do not have underinsured motorist coverage. If she files a bankruptcy, that's a big problem except in very rare instances. I guess all you can do here is follow your attorney's advice.. Best to you and sorry it's working out this way for you.
It's not a question of suing right now, unless the statute of limitations is almost up, but am a matter of seeing an personal injury first. There may be other sources of insurance to consider. You should be able to get a free initial consultation.
When I first was reading my thought was if she just wanted the bills paid and maybe something extra, she could do it herself. However, reading more about the injuries and continued care, she should get an attorney.
So very sorry to hear this. You want someone that does nursing home negligence cases. I don't in the Cleveland area anymore but we have several excellent ones in the Columbus that do this statewide. Find someone there or you can contact me I can give you a referral.