I need a more recent study than the (Bennett & Kalish, 2006) survey of 300 teachers showing that one teacher had taken a course focused on homework and that only 18% had attended professional development.
A quick glance through the second edition of Cathy Vatterott's book Rethinking homework: Best practices that support diverse needs (published by ASCD) and I could find no mention of training for teachers on designing homework.