There should be some way to get the system to actually load the newer version of libxml2 from a "keg"

Thank you for explaining the situation. I barely grasp the problem, let alone the solution. I find people on other sites fixing similar sounding issues with the command:

brew link --force libxml2

I tried it to see what happens:

brew link --dry-run libxml2
Would link:
/usr/local/bin/xml2-config
/usr/local/bin/xmlcatalog
/usr/local/bin/xmllint
/usr/local/include/libxml2
/usr/local/share/aclocal/libxml.m4
/usr/local/share/doc/libxml2-2.9.7
/usr/local/share/gtk-doc/html/libxml2
/usr/local/share/man/man1/xml2-config.1
/usr/local/share/man/man1/xmlcatalog.1
/usr/local/share/man/man1/xmllint.1
/usr/local/share/man/man3/libxml.3
/usr/local/lib/cmake/libxml2
/usr/local/lib/libxml2.2.dylib
/usr/local/lib/libxml2.a
/usr/local/lib/libxml2.dylib
/usr/local/lib/pkgconfig/libxml-2.0.pc
/usr/local/lib/python2.7/site-packages/drv_libxml2.py
/usr/local/lib/python2.7/site-packages/libxml2.py
/usr/local/lib/python2.7/site-packages/libxml2_python-2.9.7-py2.7.egg-info
/usr/local/lib/python2.7/site-packages/libxml2mod.so
/usr/local/lib/xml2Conf.sh

If you need to have this software first in your PATH instead consider running:
  echo 'export PATH="/usr/local/opt/libxml2/bin:$PATH"' >> ~/.bash_profile

/usr/local/include/libxml2 looks interesting because I don't have it and can't find those links when looking for some of them. But I do have /usr/bin/xmllint already:

xmllint --version
xmllint: using libxml version 20904

I don't know what forcing that link will do to the system, what it will break, how to unforce...