How do I Maintain Scroll Position when a node is double clicked

You can use the method ScrollNodeIntoView(Node node)of UltraWebTree. Please take a look at the code below:
protected void Button1_Click(object sender, EventArgs e)
{
Node node = new Node();
node.Text = "isdgnfiuaswbgfiouwsebgibseri node";

Node node1 = new Node();
node1.Text = "kjnhfiosenhfoinseopi node";

node.Nodes.Add(node1);

UltraWebTree1.Nodes.Add(node);

UltraWebTree1.ScrollNodeIntoView(node);

}