Yes, you're right: God certainly doesn't want His children to argue and fight over minor differences in belief. Instead, the Bible says, we should "love one another deeply, from the heart" (1 Peter 1:22).
Admittedly, churches and Christians do disagree sometimes about minor issues–but the Bible is clear about the central truths of the Gospel, and they should be our focus. Satan is delighted when Christians can't get along with each other (whatever the reason) because he knows that it blunts our witness and diverts us from God's plan for our lives. I've always tried to follow a principle I heard many years ago: In essentials, unity; in nonessentials, liberty; in all things, love.
What should you do? First, before you and your cousin get together the next time, take time to pray about your visit, and ask God to help you both avoid a contentious spirit. Instead, ask God to help you have true fellowship with each other–perhaps recounting what God has been doing in your lives recently, or sharing a problem and asking your cousin to pray about it.
In addition, remember that it usually takes two to argue–so ask God to help you guard your tongue and avoid responding. The Bible wisely says, "A gentle answer turns away wrath, but a harsh word stirs up anger" (Proverbs 15:1).