It isn't related to marriage.
Alison's answer is probably right.
Another possibility is that "detergent commercial" might mean "a soap opera." In the 1940s, 50s, and 60s, radio and television carried many daily drama programs. Each episode was only 30 minutes long. Every day, you would get a little bit of a long story.
In those days, in the United States, programs often had a single "sponsor." The sponsor paid for the whole show. All the commercials in the show were for the same sponsor. Since these shows were watched by housewives, many of them were sponsored by companies selling soap, detergent, and cleaning products. They became known as "soap operas."
Either way, the speaker says she feels as she is a character in a TV program, instead of a real person with a real life.
(This could be a complicated joke, because, of course, she really is).