You are correct in stating that Illinois Small Estate Affidavits can be used when "probate assets" are less than $100,000.00. However, with that said the person executing the Affidavit can become liable if they misuse or misapply the assets that are obtained. When you mention that there are minors involved things become more complicated and, thus, I strongly recommend that you do not attempt to navigate this process without an attorney.
This is not a "do it yourself" project!
A small estate affidavit is signed by the person handling the administration. It does not need to be filed with the court or notarized. However, many banks and other institutions will only accept notarized documents. So it's generally best to have it notarized and save yourself some hassle.
I agree with the other attorneys on the minor beneficiary issue. That adds complication, and I suggest you contact an attorney to discuss it.
This answer does not constitute legal advice and you do not have an attorney-client relationship with me or my firm. I am admitted to practice law only in the state of Illinois. All answers are general in nature and based on common legal principles. You should not rely on this answer alone and should seek the counsel of an attorney for specific guidance on your legal issues.