Thousands of New York City nurses were back on the picket lines as they walked out for a second day from their jobs at some of the city’s leading hospitals. The union on Tuesday also accused one hospital, Mount Sinai, of illegally firing three nurses. Another hospital, Montefiore Medical Center, criticized what it described as the union’s “reckless demands” and “troubling proposals” in contract talks. The walkout involves about 15,000 nurses at major hospitals including NewYork-Presbyterian. The nurses are seeking better pay and staffing levels. The hospitals have brought on replacement workers to fill the labor gap.