That could very well be, Harlow. It's been a long time since those days and in 1966 I was only five years old, well, until I turned six in JuneLOL. I don't know why I thought Carol was on Lucille Ball's show. Maybe I'm thinking of another sitcom she might have been a guest on too. I remember the Mothers-In-Law well as a kid too. It used to come on Sunday nights on NBC. In fact I remember reading about Roger C. Carmel's death and remembering him from those old episodes of the show. Ironic that you mention Jesse White too. I bought a DVD with four of the old Francis, the Talking Mule movies a few days ago. And he was in one of them. Who could ever forget his portrayal as the lonely Maytag repairman? ha ha.

Carol's 1953 appearance on the Berle-Buick Show is listed on IMDb, it's #132 on her tv credits near the very bottom of her "As Herself - TV" credits. She's terrific on this show which is on a number of vintage tv compilation budget dvd sets.
Carol never appeared on any of Lucille Ball's series or worked with Gale Gordon. I am thinking you may be remembering the pilot "The Carol Channing Show" from 1966 which I probably aired as a "special" even though the series was not picked up. It was produced by Desi Arnaz and is very much a Lucyesque sitcom with Carol having an adverserial relationship with brother-in-law Jesse White very much like Lucy's interactions with Gale. This program is a bonus feature on the MOTHERS-IN-LAW dvd set (which was also produced by Arnaz).