Will I be committing a sin if I refuse to clean the house of my husband's father, who drinks alcohol and engages in prostitution, knowing that my husband and his mother are asking me to do so? And would my husband be disobedient to his parents if he supported me in my refusal?

You are not obligated to serve your father-in-law, especially since he has daughters. However, obeying your husband in this matter is an act of kindness and benevolence, and there is no sin upon you if you do not do it. Your husband must obey his parents and he would sin if he disobeys their command, unless it is a sin. He must be kind to them, especially in their old age. If his parents order him to sweep the house, he must do so, either by himself or through someone else. The most virtuous act of filial piety is for him to strive to advise his father and call him to abandon forbidden acts with gentleness and good words.