OK this table shows that XP can install up to MSIE v8.
SketchUp 2015 requires MSIE v9+.
This is because the 3D Warehouse now has WebGL viewers for the models, and they want the build-in Components Browser to be able to render these WebGL views, and do other nifty things that rely upon the newer versions of MSIE.
But none of that matters to your install. Your kids will just need to be satisfied with the components samplers provided with the install.
So, without doubt, it is best to install SketchUp 2014 Make, which has many bug fixes over v2013, and also has Ruby v2.0 which has unicode string support, and the whole Ruby Standard Library to better support plugins.
The “reduction of support” for XP has to do with it being stuck with MSIE v8, with regard to the web functions. But your kids won’t be using the built-in web functions anyway. (These web functions can always be worked around by using Chrome to manually download models from 3D Warehouse, or manually download plugins from Extension Warehouse and install them manually via a button in the Preferences dialog. Say if the kids can get to a Public Library with WiFi, or a friends house where they can plug into a router, or whatever.)
(When SketchUp 2016 comes out, I will not be supporting plugins on any old SketchUp version that has Ruby 1.8.x. Just too much of a pain in the butt, too many issues to workaround, etc. I also expect many other plugin developers to follow suit.)