I have a source xml like following:
There are two problems in your XSLT. Firstly, where you match the s1 and s2 elements, you are not subsequently trying to apply templates to any attributes. You need to replace this statement
<xsl:apply-templates select="* | node()"/>
With this statement
<xsl:apply-templates select="@* | node()"/>
Secondly, you don't have any templates to match such attributes. You need a template like so:
<xsl:template match="@s1:*">
<xsl:attribute name="t1:{local-name()}">
<xsl:value-of select="." />
</xsl:attribute>
</xsl:template>
Try this XSLT
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns="http://sample.com/s"
xmlns:s1="http://sample.com/s1"
xmlns:s2="http://sample.com/s2"
xmlns:t1="http://sample.com/t1"
xmlns:t2="http://sample.com/t2"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
exclude-result-prefixes="s1 s2">
<xsl:output method="xml" encoding="UTF-8" indent="yes"/>
<xsl:strip-space elements="*"/>
<xsl:template match="/">
<SampleRequest
xmlns="http://sample.com/t"
xmlns:t1="http://sample.com/t1"
xmlns:t2="http://sample.com/t2"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<xsl:attribute name="xsi:schemaLocation">http://sample.com/t targetSchema.xsd</xsl:attribute>
<xsl:copy>
<xsl:apply-templates select="@* | node()"/>
</xsl:copy>
</SampleRequest>
</xsl:template>
<xsl:template match="s1:*">
<xsl:element name="t1:{local-name()}">
<xsl:apply-templates select="@* | node()"/>
</xsl:element>
</xsl:template>
<xsl:template match="@s1:*">
<xsl:attribute name="t1:{local-name()}">
<xsl:value-of select="."/>
</xsl:attribute>
</xsl:template>
<xsl:template match="s2:*">
<xsl:element name="t2:{local-name()}">
<xsl:apply-templates select="@* | node()"/>
</xsl:element>
</xsl:template>
<xsl:template match="@s2:*">
<xsl:attribute name="t2:{local-name()}">
<xsl:value-of select="."/>
</xsl:attribute>
</xsl:template>
</xsl:stylesheet>
When applied to your sample XML, the following is output:
<SampleRequest
xsi:schemaLocation="http://sample.com/t targetSchema.xsd"
xmlns:t1="http://sample.com/t1"
xmlns:t2="http://sample.com/t2"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
xmlns="http://sample.com/t">
<t1:customer t1:firstName="Jim" t1:lastName="Ellison"/>
<t2:address> 123 test street </t2:address>
</SampleRequest>