The title makes use of some Christianese: "Vertical" as in the relationship with God, and "Horizontal" as in relationships with others. It is the Christianese I am critiquing, not the relationships themselves (except for, in part, the latter).
I do not think there are supposed to be "horizontal" relationships in this way. Many sermons acknowledge the point I mean to make here, actually. We do say that if your relationship with God is not right, then your relationships with others won't be either, but we are not so clear on why this is.
My larger point is not often noted. We should have nothing apart from God. This means that in relating to others, we are relating in Christ. Our "horizontal" relationships take place through our "vertical" relationship. To have the mind of Christ is to see the world as Christ sees it, which is to be united with him--into the body, the Church. To do otherwise would be to have some other mind. To see the world merely through our own eyes is pride: it is thinking we can see rightly apart from Christ. Apart from Christ we can do nothing, and we are blind. We cannot see others rightly, let alone act according as we ought, if we do not have the life of Christ in us.
And this is what it is to act in love: not merely to act in a way that we think is loving, but to act in the Spirit of love--i.e., by the power of the Spirit of God who is love. Thus all our relationships are to be vertical, or perhaps zig-zag. Indeed, since we cannot see rightly apart from Christ, our horizontal relationships are relationships of falsehood. They are not true relationships at all, but merely a relating of self to others, but the others are not truly there.
You think your relationships are broken? You do not know how much! Yet Christ knows all about you, and knows what is good for you, and for those you love. And Christ provides the grace to go on, for he has broken down the barrier of sin which keeps us apart from him, and him from the world, and so in him we find union--truly?--yet so rarely shown in our Churches, our union in Christ is one of the most important things we should be striving to reveal in our life together. We cannot manufacture this revealing of the unity of the body of Christ, though, since we do not know how to act, but if we are under the headship of Christ, then he will guide us into the way we should go. 1 John 4:10, "In this is love, not that we have loved God but that he loved us and sent his Son to be the propitiation for our sins." and it remains this way even in the love of the Christian for others: it is still the love of God for us and sending his Son to be the propitiation for our sins. Even our love for God is by our union with Christ.