Google multilingual sitemap issue

Question

I have a sitemap issue. I am working on a multilingual website and I'm trying to use the Google method to indicate alternate language pages, as it is described here : https://support.google.com/webmasters/answer/2620865?hl=en.

You can see my sitemap here : http://preprod.fabric-a.fr/princesse-nomade/sitemap.xml It seems that this sitemap is broken, and I don't understand why, it respects the example given by google..

Curiously, when I replace xmlns:xhtml="http://www.w3.org/1999/xhtml" by "xmlns:xhtml="http://www.w3.org/1999/xhtml:link", it seems to appear not broken. But it is clearly incorrect.

I'm lost, some sitemap testers are telling me that it is correct. Others are telling me that the <priority> and <changefreq> balise are not correct regarding to the namespace used.

Is anyone has a clue to help me, I would appreciate, I find a lot of informations about sitemap, but nothing about this precise problem.

Thanks by advance for your help !

EDIT :
I'm still looking for an answer and I found this answer from this topic :
http://forum.elxis.org/index.php?topic=7575.50;wap2
It is told that the http://www.w3.org/1999/xhtml namespace doesn't support the <xhtml:link /> balise.
The namespace that should be used is this one : http://www.w3.org/TR/xhtml11/xhtml11_schema.html
I just tried, and it is well parsed by navigators. If this is correct, I really don't understand why Google gives a wrong tutorial on their own site.

I would be happy to get some advice from SEO experts about this!