Is the wife entitled to request independent housing, or is that considered a cause for her husband's disobedience to his parents?

A suitable independent dwelling for the wife is her right by virtue of the marriage contract, based on the Almighty's saying: "Lodge them [in a section] of where you dwell, according to your means, and do not harm them in order to oppress them." This does not constitute disobedience to parents. The husband must balance the rights of both parties, and the wife should help her husband in being dutiful to his parents, as part of living together honorably. If the wife is not harmed by the presence of the parents and endures the disagreements, then that is an act of benevolence.