Export XMLElements with MathML contents

Question

Setup

Here's my mathML expression:

mathML = ExportString[1/2, "MathML"]

"<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mfrac>
  <mn>1</mn>
  <mn>2</mn>
 </mfrac>
</math>"

and an XMLElement:

xml = XMLElement["tag", {}, {"data", mathML}]

Task and the problem

which I'd like to Export(String) without manipulating mathMLcontents but it converts some symbols:

ExportString[xml, "XML"] 

"<tag>data&lt;math \
xmlns=&apos;http://www.w3.org/1998/Math/MathML&apos;&gt;
 &lt;mfrac&gt;
  &lt;mn&gt;1&lt;/mn&gt;
  &lt;mn&gt;2&lt;/mn&gt;
 &lt;/mfrac&gt;
&lt;/math&gt;</tag>"

Expected result:

while I'd like to get:

"<tag>data<math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mfrac>
  <mn>1</mn>
  <mn>2</mn>
 </mfrac>
</math></tag>"

---

Solution(?)

I can get this with

ExportString[xml, "XML",  "Entities" -> {"<" -> "<", ">" -> ">", "'" ->"'"}]

but is this the right approach? If not, can I restrict this to only MathML expressions somehow?

A problem with solution:

The problem is that if those symbols are somewhere outside MathML expression, the resulting XML document will have incorrect structure:

ExportString[
  XMLElement["tag", {}, {"1 > 2"}], 
  "XML", 
  "Entities" -> {"<" -> "<", ">" -> ">", "'" -> "'"}
]

"<tag>1 > 2</tag>"

I suppose it is not acceptable. I'm not sure though.

Answer 1

After a bit, I hit upon a solution involving a round-trip through the import/export subsystem. First, it is helpful to have everything in the same representation, so we need to put the mathml into XMLElement form, e.g.

mathml = ImportString[ExportString[1/2, "MathML"],
 {"MathML", "XMLElement"}]
(*
 XMLElement["math", {"xmlns" -> "http://www.w3.org/1998/Math/MathML"}, 
 {XMLElement["mfrac", {}, {XMLElement["mn", {}, {"1"}], 
   XMLElement["mn", {}, {"2"}]}]}]
*)

Then, you can combine them as you wish,

xml = XMLElement["tag", {}, {"data", mathml}]
(*
 XMLElement["tag", {}, {"data", 
  XMLElement["math", {"xmlns" -> "http://www.w3.org/1998/Math/MathML"}, 
   {XMLElement["mfrac", {}, {XMLElement["mn", {}, {"1"}], 
  XMLElement["mn", {}, {"2"}]}]}]}]
*)

and when exported

ExportString[xml, "XML"]
(* "<tag>
 data<mathxmlns='http://www.w3.org/1998/Math/MathML'><mfrac><mn>1</mn><mn>2</mn></mfrac>
 </math></tag>"
*)

Note, it appears to lose formatting, and initially I was under the impression that the text could not be a sibling to an xml element, but re-reading the xml spec, implies that it is, instead, being treated as an inline element.