Is it permissible for my wife to use the financial limit designated for my dental treatment or the dental treatment of one of our children after she has exhausted her own insurance limit, knowing that she needs the treatment and it is not for cosmetic purposes?

If the use of the wife's (death) limit by the husband or one of her children is permitted in the insurance policy contract, then there is no objection to it. Otherwise, it is not permissible, due to the generality of the Hadith: "Muslims are bound by their conditions."