First, I am sorry to hear of your trying and very sensitive situation. I assume your sister is an adult (over 18). The reason people may be repeatedly telling you that nothing legally can be done by you, personally, to have her admitted against her will, is that she is an adult and you are not her appointed power of attorney for healthcare or "guardian." Am I correct? Also, even if you had power of attorney over those types of decisions, it does not sound like she has done anything to trigger your "authority" to make decisions on her behalf -- at least from the standpoint under the law. Does your sister live with you, and in turn, that is why you worry about the safety of your children? Obviously safety of your children most important. If you think your sister poses any type of danger to them, you have the right and, perhaps, obligation to avoid that type of situation. Under Illinois law, your sister cannot require that she have "visitations" with her nieces/nephews.
Unless you have any other facts that you left out, as her sibling, there is not much you can do. In the event her actions continue to deteriorate, and if she should ever get into trouble with the law, that may be the event that triggers the State to evaluate her mental capacity if it is in question. Good luck to you.