The mother of a baby who suffered brain damage during birth at an Oak Park hospital will receive $51 million after a monthlong trial that shattered the existing state record for a birth-injury verdict.Jurors awarded $100.6 million to the plaintiff on Tuesday. Before Cook County Associate Judge Robert E. Senechalle Jr. entered that verdict, the hospital and the mother reached a high-low agreement with a high bound at $50 million and a low at $20 million, according to Keith A. Hebeisen of Clifford Law Offices, one of the …