In daystar it is reasonable to infer that the mother

I’m guessing is the poem Daystar by Rita Dove.

Well the correct analysis about it is that she is tired and she takes advantage of the little free time she has for herself to take a chair and sit outside looking at the nature or at nothingness until either she closes her eyes and feels alive or her children wake up and call for her again, she also lies awake while in bed with her husband thinking about the time she´s spent being a mother and changing diapers, she feels trapped and these very few moments for herself are the only window of happiness she gets.  

I don’t know what you want to infer, if either she dies or something but is just that, she´s just tired.

what motivates odysseus to tell a lie to the cyclops

type of error:

the error in the sentence is a "dangling modifier". a dangling modifier is a phrase, word or clause that "dangles" because there is not target to modify. in this case, "after mopping the floor" is the dangling modifier since it has no word to modify. the noun "house" cannot mop the floor; therefore there is a mistake in the writing of the sentence.