How to control node placement in graphviz (i.e. avoid edge crossings)

You could create an invisible constraint, to cause the red node to appear to the left of all other nodes.

redNode -> leftmostNode [style=invis];

Before:

After:

I like @smokris' [style=invis] trick for persuading graphviz to put things where you want them, by adding edges which affect layout but aren't visible.

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Another trick is the constraint attribute, which lets you add edges which are visible but don't affect layout.

If adding a new edge messes up your graph, set [constraint=false] on that edge: now graphviz will ignore it when placing nodes. 🙂

If false, the edge is not used in ranking the nodes. For example, in the graph

digraph G {
    a -> c;
    a -> b;
    b -> c [constraint=false];  
}

the edge b -> c does not add a constraint during rank assignment, so the only constraints are that a be above b and c, yielding the graph: