Yes, I have two different sites 2012 and 2013,both having a form library called Activities.
When you say “When you re-open an existing XML...”, you mean a filled form instance that I can download from the library on my local drive and open in a text editor? I'll try but unfortunatly I can't make other attemptes now, my services are not working after some hour.
For the other problem is that I have notice this:
When I publish the two templates (after making the change of the name in one of them, using the “Form Template Properties”), I look in both libraries and click in the link Edit Template. In both templates opened, if I go again in the “Form Template Properties” I see the Name is now Activities (name of the Library) and the ID is urn:schemas-microsoft-com:office:infopath:Activities:-myXSD-2011-04-14T16-03-46.
If instead I open the templates that I have saved on my PC, they have still the Name and ID I have set up before publishing, two different ones.
Maybe it is not a problem but I was wondering why about it, just to make sure that the users could work with both 2012 and 2013 form libraries and the modifications they will do in forms of 2012, won't be instead submitted on 2013 (because of the apparently same IDs, looked from inside the libraries).