Legal Question in Wills and Trusts in Illinois

No.

Assuming that there is no will, then no. If there is a will, you would have to look at the will to see what the decedent's wishes were with respect to her grandchildren.

Regarding mother's heirs...

Any children that survived mother (i.e., that lived beyond mother's death) are heirs. The descendants of such children are NOT heirs.

However, since those children who did NOT survive mother (i.e., did NOT live beyond mother's death) cannot be heirs, certain descendants of those children are heirs.

I recognize how this can be a little confusing. It's more helpful if you visualize this as a family tree and imagine it stopping at those who are living. Please call me for a free consultation if you'd like to discuss this further.