Red-black trees are conditionally defined as left. How can I do it right?

Question

Red-black trees are conditionally defined as left. How can I do it right?

As the name says, red-black trees created using modified binary search trees have an arbitrary restriction that all red links are left-handed. I made a basic program for red black trees (java), and I am curious how to change this, because it seems that it will be simple, but all the solutions elude me.

My code is close to what is in this PDF file: http://www.cs.princeton.edu/~rs/talks/LLRB/LLRB.pdf

For example, here is the treeRepair method on the left side:

private TreeNode<Key, Value> treeRepair(TreeNode<Key, Value> node)
{
    if (isRed(node.right) && !isRed(node.left)) node = rotateLeft(node);
    if (isRed(node.left) && isRed(node.left.left)) node = rotateRight(node);
    if (isRed(node.left) && isRed(node.right)) flipColours(node);

    node.size = 1 + size(node.left) + size(node.right);

    return node; 
}

This works great. It starts at the end of each insert and delete. There is a modified version with a flip that actually works for a while.

private TreeNode<Key, Value> treeRepair(TreeNode<Key, Value> node)
{   
    if (isRed(node.left) && !isRed(node.right)) node = rotateRight(node);
    if (isRed(node.right) && isRed(node.right.right)) node = rotateLeft(node);  
    if (isRed(node.left) && isRed(node.right)) flipColours(node);

    node.size = 1 + size(node.left) + size(node.right);

    return node; 
}