i would say, in this context that ‘detergent commercial’ refers to an advert on television for laundry powder or dishwashing liquid where the home and marriage is perfect, and a smiling woman happily washes clothes and does chores with perfect makeup. The message of course is how happy women are to do the domestic chores, and the homes are perfect and conflict free. The wife is depicted as the ‘helpmeet’ to the husband. In today’s western society this is not the norm any longer with the majority of marriages have both partners with careers, and sharing domestic duties.

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).