I'm not sure if it's the most elegant solution in the world, but I think this would probably do what you're after:
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<!-- If the element exists, do what you want to do -->
<xsl:template match="element1">
<xsl:copy>Changed1</xsl:copy>
</xsl:template>
<xsl:template match="element2">
<xsl:copy>Changed2</xsl:copy>
</xsl:template>
<xsl:template match="element3">
<xsl:copy>Changed3</xsl:copy>
</xsl:template>
<!-- If the element doesn't exist, add it -->
<xsl:template match="group">
<xsl:copy>
<xsl:apply-templates/>
<xsl:if test="not(element1)">
<element1>Changed1</element1>
</xsl:if>
<xsl:if test="not(element2)">
<element2>Changed2</element2>
</xsl:if>
<xsl:if test="not(element3)">
<element3>Changed3</element3>
</xsl:if>
</xsl:copy>
</xsl:template>
<!-- Identity transform -->
<xsl:template match="@*|node()">
<xsl:copy>
<xsl:apply-templates select="@*|node()"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>
Anything which isn't explicitly matched should just copy across untouched.
Of course, if the values are constant (that is, element1, element2 and element3 will always have the same values regardless of whether they're new or updated) then you can have something simpler:
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<!-- If the element exists, remove it -->
<xsl:template match="element1 | element2 | element3"/>
<!-- Now put in your preferred elements -->
<xsl:template match="group">
<xsl:copy>
<xsl:apply-templates/>
<element1>Changed1</element1>
<element2>Changed2</element2>
<element3>Changed3</element3>
</xsl:copy>
</xsl:template>
<!-- Identity transform -->
<xsl:template match="@*|node()">
<xsl:copy>
<xsl:apply-templates select="@*|node()"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>
Which essentially removes the original "element" nodes and puts yours in in their place.