I am sorry for your loss. The minor children need to be protected here. In Illinois the statute is very specific
Every such action shall be brought by and in the names of the personal representatives of such deceased person
Because he was not married at the time of his death consider the statute language
the amount recovered in every such action shall be for the exclusive benefit of the surviving spouse and next of kin of such deceased person
The kids are next of kin and certainly must be protected.
Alan James Brinkmeier
As I'm guessing you've gathered from the others, what happens is that someone has to be chosen by the court to be the representative. Being the representative in a wrongful death suit like this really just means that you sign certain documents which are necessary to move the case along. Settlements in wrongful death cases require court approval in Illinois, so no matter what the representative thinks any resolution of the case or distribution of the proceeds needs to be approved by a judge. The important thing is for the family to find an experienced, competent lawyer to handle the case. Once you find that person, he or she will get the family together, explain the process, and show everyone how they'll be involved and informed.
I'm sorry for your loss. Pick a really good lawyer and the rest will work itself out. Best of luck.