First:
git merge origin/remote_branch
should probably read git merge --no-commit to make sure Git does not commit these changes if there are no merge conflicts, otherwise your next steps do not make much sense.  Note that there will be no merge conflicts at all if the --theirs commit has changed some pom.xml files and you have not changed them, or if Git thinks it successfully merged your changes and theirs.  (If you want to use theirs in one of these cases, that's also a bit tricky, but you seem to want to use the --ours versions always.)
Next:
git checkout --ours **/pom.xml pom.xml
This relies on your shell (presumably bash or similar) to expand ** the way you want; you might want to quote the asterisks, and make Git do the glob expansion.  This could affect your particular case though, and I'm not sure how Git handles this during a merge conflict, so before you do anything like that, you would want to experiment carefully.
This works great except if a pom.xml file has been removed in the local branch. After running command #2 above we get an error:
d:\code>git checkout --ours **/pom.xml pom.xml
error: path 'blah/pom.xml' does not have our version
Right: for this case, if you want to keep the deleted file deleted, you need to override Git's default action of choosing to keep their version in the index and work-tree.
Let's jump into the Git-specific part of all of this, the index.  Remember, Git's index is where you build the next commit you will make.  During a merge, it's also where you resolve conflicts.
Entries in the index during a merge
In the normal (non-merging) cases, the index has one entry for every tracked file.  If file F is in the current (HEAD) commit and the work-tree, the index has an entry for F.  Initially this index entry version matches the HEAD version.  You modify the file in the work-tree, then git add the work-tree version to copy it into the index in place o the HEAD version; and then the next git commit will save the index version.
During a conflicted merge, where file F has a conflict, the index has up to three entries for F instead of the usual one.  These entries go in slots number 1, 2, and 3.  (Slot zero is reserved for the normal, not-conflicted entry.)  Slot 1 is for the merge base version.  Slot 2 is for --ours, and slot 3 is for --theirs, and you can just use these names for 2 and 3, but there's no name for slot 1.
A merge conflict occurs when:
- the same line(s) were modified in ours and theirs, with respect to the base version (this is a modify/modify conflict), or
- there is no base version, just ours and theirs (this a create/create conflict), or
- we removed the file and they changed something, even just the name (this is a delete/modify or delete/rename conflict), or
- they removed the file and we changed something: this is also a modify/delete or rename/delete conflict, with the partners swapped around.
For the modify/modify conflict, all three slots are populated.  For the other three types of conflict, one slot is empty: the merge base slot is empty (create/create), or --ours is empty (delete/X), or --theirs is empty (X/delete).
The git checkout --ours step fails when the --ours slot is empty.  It succeeds when the --ours slot is non-empty: it extracts the --ours version into the work-tree.
Git's default action on any delete/X or X/delete conflict is to leave, in the work-tree, whichever version survived.  That is, if it's slot 3 (theirs) that's empty, the work-tree file matches the slot 2 entry, but if it's slot 2 (ours) that's empty, the work-tree file matches the slot 3 entry.
You could choose to handle this by scanning for empty "slot 2"s and git rming the file for this case:
git ls-files --stage | fancy-script-or-program
If you write this as, say, a Python program, use git ls-files -z --stage to make it easily machine-parseable.  You could even stop using git checkout --ours at all, and stop depending on shell or Git globbing, and code the rules for resolving pom.xml files entirely in the script.
Essentially, you might read through the entire index, looking for files whose base-name (everything after the final /) matches pom.xml:
- If there is a stage-zero entry, Git thinks it resolved the file correctly.  Compare the hash ID with the one in the - HEADcommit, because Git may not have actually resolved the file correctly after all; in this case, replace the index blob hash with the one from the- HEADcommit.  See the- git update-indexdocumentation for details.  You should be able to use- --cacheinfo, although I have not tested this with unmerged index entries.
 
- Otherwise, there are stage 1, 2, and/or 3 entries.  If there is a stage 2 entry, use it as the resolution, i.e., feed it to - git update-indexas above.  If there is no stage 2 entry, use- git update-indexto remove the entries (using- 0for the mode, and anything, including the all-zeros hash, for the hash; the hash is irrelevant if the mode is 0).
 
Once you have done this with all the pom.xml paths, any remaining non-zero stage index entries indicate a merge conflict you should pass back to your user.  Otherwise, you may be ready to commit.
(A quick scan of http://gitpython.readthedocs.io/en/stable/reference.html#module-git.index.base suggests that this could be done fairly easily in GitPython, but I have no experience with using it.)
Final caveat: I have no experience at all with Maven, but I gather that pom.xml files are XML files that control various things and that Git merges poorly (the last is true of pretty much all XML files).  It's not at all clear to me that just using the "ours" version is correct, though.