Legal Question in Landlord & Tenant Law in Illinois

You can threaten calling the building department, but here are two things: mice come in in the fall, they get into the tiniest of cracks, it often takes several efforts to completely eliminate them, and YOU have to show you're keeping the inside of the place CLEAN. An attorney will want to see your lease but assuming the right language is there the attorney can write a letter demanding the work be done, mention the child, and suggest that if the work is not done you'll consider the place not habitable and move out as a "constructive eviction"...something like that.

While I am an active member of the Illinois Bar, this Answer is intended solely as a courtesy to the Questioner based on an incomplete set of facts, so that the Questioner can be encouraged to obtain proper and complete legal advice based on all of the necessary facts.

This is not meant as a definitive answer but a general narrative to assist you in heading in the right direction. Any law cited or referred to specifically or generally may or may not apply to a specific set of facts. We nevertheless hope this is of some help to you.