Complex sentence: In December, 1950, when CBS agreed to produce a TV pilot starring Lucille Ball and her husband, Desi Arnaz, Lucy insisted on Oppenheimer to head up the project.
Split into simpler sentences: In December, 1950, when CBS agreed to produce a TV pilot starring Lucille Ball and her husband, Desi Arnaz. Sr., Lucy insisted on Oppenheimer to head up the project.