We understand that you are seeking God's will in your relationship and we commend you for that. It is crucial to have God at the center of any relationship, especially one that could lead to marriage. Let us first address your concerns with relevant biblical principles and prayers.
Firstly, it is important to note that God's design for relationships is that they should be between a man and a woman, with marriage as the ultimate goal.
Your desire for mutual respect is biblical. The Bible tells us in Ephesians 5:21 to "be subject to one another, in the fear of Christ." This mutual submission is key in any godly relationship. It is not just about one person submitting to the other, but both yielding to each other out of reverence for Christ.
However, we want to address something important. You mentioned that he wants you to submit, but you want him to respect you. Submission in a biblical context is not about one person being dominant over the other, but rather both parties mutually yielding to each other and ultimately to Christ. Make sure neither of you seek control or dominance over the other.
The Bible says in Colossians 3:18 WEB, that wives should submit their husbands, as the Lord would have them do so. Not that women should submit to men but as Colossians 3:19 states husbands, their love be not harsh to their wives. We see throughout the Bible that God has called on men to care for the women in their lives. Colossians 3:19 WEB, Husbands, love your wives, and do not be harsh to them.
Regarding your desire for him to have eyes only for you, that is also biblical. In the Song of Solomon, we see a picture of exclusive love and desire between a husband and wife. However, it is important to ensure that this relationship is aligned with God's will. If it is not, then it is wise to pray that God would remove him from your life, as you have done.
Let us pray together:
Dear Heavenly Father,
We come before You in the name of Jesus, lifting up our sister in Christ. We pray for Your will to be done in her relationship. If this man is not Your will for her, we ask that You would remove him from her life. If he is, we pray that You would give them both a spirit of mutual respect and submission, that their relationship would glorify You and lead to a godly marriage. We pray if there are any themes of control or dominance that should not be.
We ask that You would guide them both, giving them wisdom and discernment. Heal any past hurts and help them to move forward in Your will. We ask this in the name of Jesus Christ, the only name by which we can be saved. Amen.
Lastly, we want to remind you that God's design for intimacy is within the bounds of marriage. If this is not already the case, we encourage you to abstain from sexual immorality, as the Bible teaches in 1 Thessalonians 4:3 WEB, "For this is the will of God: your sanctification, that you abstain from sexual immorality."
We are here for you, praying and believing with you for God's best in your life and your relationships. Keep trusting in the Lord with all your heart. Make sure to keep Jesus Christ in your relationship the name of Jesus Christ, the only name by which we can be saved. Believe in the name of Jesus Christ and you will be saved. As believers in Jesus Christ it is only by His name we have access to God. Is the fiancee a Christian believer in Jesus Christ? That is another important question to address.
Prayer Focus: God, Thank You for loving me. Thank You for loving me, Jesus. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, soul, mind, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
