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I believe it is "Ralph Goes Hollywood" from 10/4/69---Bing Crosby, Maureen O'Hara, and Bert Parks are the guests as the Honeymooners head for Hollywood to claim their song writing prize.

I think you're right. I didn't look at the clip. I guess they are referring to the Hollywood trip which was a few weeks prior to that show. That's the only Honeymooners Mike Douglas appeared in, although I know of a Jackie Gleason Show he was a guest on. This is the show:

http://www.imdb.com/title/tt0614042/

Are you sure it's not "The Honeymoon Is Over" from 11/1/69?
Oh, it's from "The Honeymoon Is Over" all right. I.I.N.M., the makeup artist in that bit was Jan Miner (a.k.a. "Madge" in the Palmolive ads).