SPRINGFIELD — Northwest Chicago Democrat Sen. John G. Mulroe will resign from his post as a lawmaker to fill a Cook County Circuit Court judicial vacancy in the 10th Subcircuit.Mulroe will be filling the seat left by Circuit Judge Thomas Allen, who retired from the bench.This was not Mulroe’s first attempt to join the bench. He ran for a 10th Judicial Subcircuit seat in 2008.“I lost by about 1,300 votes …