I have solved my problem with by handling the enter and exit edit.  I found that if I change the alignment to left and RightToLeft = yes then the edit operates as expected.

Here is the code if anyone else is interested.

public class UltTextEditorRTL : Infragistics.Win.UltraWinEditors.UltraTextEditor
    {
        public delegate void SetTextAlignmentHandler(Infragistics.Win.HAlign align);
        bool bIgnoreEditor = false;

        public UltTextEditorRTL()
        {
            this.BeforeExitEditMode += new Infragistics.Win.BeforeExitEditModeEventHandler(this.BeforeExitEdit);
            this.BeforeEnterEditMode += new System.ComponentModel.CancelEventHandler(this.BeforeEnterEdit);
        }

        private void SetTextAlignment(Infragistics.Win.HAlign align)
        {
            System.Diagnostics.Trace.WriteLine("SetTextAlignment");
            Appearance.TextHAlign = align;
           
        }

        private void BeforeEnterEdit(object sender, CancelEventArgs e)
        {
            System.Diagnostics.Trace.WriteLine("BeforeEnterEdit-Start");
            if (Appearance.TextHAlign != Infragistics.Win.HAlign.Left &&
                RightToLeft ==  System.Windows.Forms.RightToLeft.Yes)
            {
                BeginInvoke(new SetTextAlignmentHandler(SetTextAlignment), Infragistics.Win.HAlign.Left);
                bIgnoreEditor = true;
            }
            else
            {
                bIgnoreEditor = false;
            }
            System.Diagnostics.Trace.WriteLine("BeforeEnterEdit-End");
        }

        private void BeforeExitEdit(object sender, Infragistics.Win.BeforeExitEditModeEventArgs e)
        {
            System.Diagnostics.Trace.WriteLine("BeforeExitEdit-Start");
            if (Appearance.TextHAlign != Infragistics.Win.HAlign.Right &&
                RightToLeft == System.Windows.Forms.RightToLeft.Yes &&
                !bIgnoreEditor)
                BeginInvoke(new SetTextAlignmentHandler(SetTextAlignment), Infragistics.Win.HAlign.Right);
            System.Diagnostics.Trace.WriteLine("BeforeExitEdit-End");
        }
    }

The form is set to RightToLeftLayout = true and RightToLeft = RightToLeft.Yes

The control is set to RightToLeft = RightToLeft.Yes and TextHAlignment = Right

There is not an option of changing the form, but there is no reason to have the control set to RTL if that is causing an issue.  I will see if that makes a difference.