What does 1984 tell us about the importance of controlling relationships between man and woman in order for totalitarian regimes to maintain power?
A good place to look for the answer to this question is in looking at the relationships that Winston has had in his life, most specifically with Julia. When he is with Julia for the first time, they describe their act of passion as "a political act," or a form of rebellion. They were together merely to make a point and express their hatred and rebellion towards the Party. Later, in conversations with Julia, she lets Winston know her thoughts on the issue. She says that the Party uses the intense passion that men and women have for each other and channels it instead into a fierce passion for the Party. The Party purposely condones and suggests marriages that will be loveless and joyless, as Winston's was; that way, any passion or intensity can be saved for Party loyalty. Human beings naturally want to love; they naturally are passionate about their relationships. So, in Oceania, relationships are devoid of that passion so that it can be used more "effectively" for Party fervor, and to solidify and strengthen the patriotism and loyalty to the Party.
For a party to maintain its power and control, it needs to save for itself humankind's most precious and intense feelings; otherwise, people get distracted with falling in love, starting families, being good parents and striving to provide for their well-being. A totalitarian regime needs all of that energy, time, focus, love and devotion dedicated to building up the state, the government, the nation and the society--not in individual pursuits. In 1984, the Party stifles and discourages close relationships through arranged marriages, approval of matches, and the Anti-Sex Junior League where young girls are brainwashed into channeling all romantic notions into passion for Party over men. As a result, you see their society filled with avidly supportive, feverishly patriotic people, directing love, passion and other emotions previously dedicated to relationships to the Party itself.
I hope that those thoughts helped; good luck!