Is the wife entitled to seek divorce because her husband does not divide his time justly between her and her co-wife, and because he chooses to reside with her co-wife most of the time, justifying this by claiming that the wife does not get along with her co-wife?

Allah the Almighty has permitted a man to marry up to four wives, provided certain conditions are met. Among these conditions is fairness in dividing nights among the wives, as a man is obligated to apportion his days equally among them. He is not allowed to favor one with more time unless the other consents. Whoever does not act justly in dividing nights has disobeyed Allah, and he who inclines to one of them will come on the Day of Resurrection with his side leaning. It is forbidden to enter upon a wife on a night that is not hers, except out of necessity. Your husband is committing a sin by not being just in the division of nights, and his excuse that you two don't get along is not a justification for his injustice. As for your request for divorce, patience, along with exerting effort to reform him, is better. You can seek help from wise people and warn him with the possibility of divorce, while also increasing your supplications for his guidance.