Complex sentence: Famous celebrity panelists Brett Somers (Klugman's wife at the time) and Charles Nelson Reilly began as guest panelists on the program, with Somers brought in at the request of Klugman, who felt she would make a nice fit on the program.
Split into simpler sentences: Famous celebrity panelists Brett Somers (Klugman's wife) and Charles Nelson Reilly began as guest panelists on the program, with Somers brought in at the request of Klugman. Klugman and Somers were married at the time, and he felt she would make a nice fit on the program.