How to move elements in an xml file within the tree

I have an xml file of the following form:

<results>
 <sequence-name>name1</sequence-name>
 <repetitions>
  <window>
   <key1>1</key1>
  </window>
 </repetitions>
 <sequence-name>name2</sequence-name>
 <repetitions>
  <window>
   <key1>4</key1>
  </window>
  </repetitions>
</results>

I would like to move the element sequence-name such that it is the first element inside window, so the output should look like:

<results>    
 <repetitions>
  <window>
   <sequence-name>name1</sequence-name>
   <key1>1</key1>
  </window>
 </repetitions>    
 <repetitions>
  <window>
   <sequence-name>name2</sequence-name>
   <key1>4</key1>
  </window>
 </repetitions>
</results>

I tried using grep to produce two files, one containing just the lines with <sequence-name>, and one with all the other lines. But I can't figure out how to insert the lines containing <sequence-name> back into the place I would like. I'm guessing there is a solution using sed/awk. I am also happy to use a tool such as xmlstarlet.

Solution

The following stylesheet should do the trick:

<?xml version="1.0"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

<xsl:template match="/ | node()">
  <xsl:copy>
    <xsl:apply-templates select="node()[not(self::sequence-name)]" />
  </xsl:copy>
</xsl:template>

<xsl:template match="window">
  <xsl:copy>
    <xsl:copy-of select="preceding::sequence-name[1]" />
    <xsl:apply-templates select="key1"/>
  </xsl:copy>
</xsl:template>

</xsl:stylesheet>

You can apply it using xsltproc stylesheet data or xmlstarlet tr stylesheet data.