The poem "The Clown's Wife" represents the difference between the personal and professional lives of people. Do you agree?

There are actually two questions implied here, so I'll give you some guidance for both.
One question is whether the reader agrees that this is the theme of the poem. I think it would be difficult to find textual support otherwise. The speaker notes the way her husband is a "king on a throne" at work and although he performs well on stage, he comes home with the "world on his shoulder." His wife then becomes the performer, doing what is needed to cheer him.
Another question is whether people generally do this—act one way at work and another way at home. Although a generalization like this could not possibly apply to every circumstance, people do (generally) feel more comfortable at home and are more themselves (good and bad). Venting about work and school, pent up all day because of social restrictions, spills out at home. True passions are shared at home. Deep conversations, which people can't necessarily have at work due to a lack of time or a lack of meaningful relationships there, happen at home as well. Additionally, every personal relationship has differing demands on a person. The dynamics of a boss/employee relationship is different, for example, than the dynamics of a mother/daughter relationship. So I do think that people generally behave differently at work (or school) than at home, but that isn't necessarily a negative thing.

This question is a standard "what do you think?" type of question, so you can feel free to agree or disagree with the statement so long as you defend it. I think the poem supports the statement because the narrator does a straightforward job of telling her readers that her husband is a "different person" at work than he is at home. The wife tells readers that the shift in personality isn't even a gradual shift. She tells readers that it happens the moment that he walks through door. He goes from being a funny, high energy kind of person to a sad and worry-filled man. I tend to agree with the poem's concept that people have their home "face" and their work face. Jobs demand that individuals behave in a certain way. Whether it's how a teacher treats kids or how a grocery bagger speaks to customers, the job demands certain behavioral protocols; however, it's not realistic that a person acts that way all of the time. The actions and attitudes that a person puts on at work are similar to getting dressed. A person puts on his suit and tie in the morning as well as the persona that goes with it. Then at home, that person switches to rugged jeans, work boots, and the persona that goes along with finally being in a place to relax and take off the work persona.