Frankly, it may not be possible to satisfy everyone, although I commend you for trying. One possibility might be to find a church that's willing to let you use its facilities, and then include the pastors of both churches in the service.
Your real goal, however, should be to look beyond your wedding day and decide where you will become active church members. (It may not be in either of the churches your parents attend, of course.) Perhaps this hasn't been an issue with you; like many people your age, you may have drifted away from church and no longer see it as important. But God gave marriage to us, and when you say your vows on your wedding day, you'll be making them not only to each other but to Him.
Why do I emphasize this? The reason is because God wants your marriage to have a solid foundation -- and that foundation is Jesus Christ. As I've often said, a good marriage actually needs three people: the husband, the wife and God. Begin your marriage the right way, by committing your lives and your marriage to Christ.
Then, as a couple, learn to walk with God every day -- reading the Bible together, praying together and discovering the joy of fellowship with others through your church. Marriage is more than warm feelings; it involves a commitment to each other -- and to God. Make it your goal to "live a life worthy of the Lord" (Colossians 1:10).