Monarchs

Who's really wearing the (metaphorical) pants? Who gets to rule the roost? Who's the power behind the throne? We have so many metaphors and sayings about power dynamics in romantic relationships that many of them have become downright cliché. Barbauld doesn't use any obvious clichés in "The Rights of Women," but she does borrow some imagery of kings and queens that was pretty common at the time to describe the power plays that can develop between men and women.

• Line 4: Lots going on in this line. The speaker isn't talking about a literal empire, so this has to be a metaphor. And the word "breast" is being used to metonymically stand in for emotions and feelings. Just to clarify: a metonymy is when two things are being compared because they are closely associated with each other, and a metaphor is when two things are being compared because they are similar. 
• Lines 7-8: We've got an extended metaphor here. The speaker isn't talking about a literal coup d'etat, or a government take-over, so when she talks about men stepping down from the throne and kissing the woman's "sceptre," she's speaking metaphorically. And we've got another metonymy, too, since the sceptre the woman carries stands in, by association, for her new power, having the men kiss the sceptre stands in metonymically for men respecting women's rule.
• Lines 17-18: The speaker continues the extended metaphor of women as monarchs—she tells women that they should do whatever necessary to make men bow down before them.
• Line 19: And the extended metaphor continues. Men are meant to be subjects—in other words, they are supposed to be ruled over by women. They aren't meant to be friends or equals.
• Line 23: The speaker tells women that they shouldn't give favors away to just anyone. They need to be even more difficult to please than "princes." So she compares women to princes through an indirect analogy.
• Line 30: More metaphor. We know that we're not talking about literally "moving" someone's heart. That would be gross and kind of messy. Nope, the speaker is being figurative again. The heart stands in metaphorically for the woman's feelings and emotions.