Git clone with user and password

While the hook is running, GIT_DIR and (if the worktree was defined explicitly) GIT_WORK_TREE are set. That means your pull won't run with the second repository in the directory you changed to.

Try git --git-dir ~/websites/testing/.git --work-tree ~/websites/testing pull; or unset git's repo-local environment with this:

unset $(git rev-parse --local-env-vars)

More info on these environment variables in man 1 git.

You will find a similar mechanism with gitolite, based on ssh and forced command.
(including ldap queries).
It don't allow interactive shell however, which could be your issue there.

The OP Frank Brenner adds:

Ah, I figured it out - the command has to be in single quotes. I suppose $SSH_ORIGINAL_COMMAND was getting expanded before git-shell was started.

That is confirmed in the gitolite forced command script is a Perl one, ending with:

# ----------------------------------------------------------------------------
#       over to git now
# ----------------------------------------------------------------------------

if ($ENV{REQUEST_URI}) {
    log_it($ENV{REQUEST_URI});
    exec $ENV{GIT_HTTP_BACKEND};
    # the GIT_HTTP_BACKEND env var should be set either by the rc file, or as
    # a SetEnv in the apache config somewhere
}

log_it();

$repo = "'$REPO_BASE/$repo.git'";
exec("git", "shell", "-c", "$verb $repo") unless $verb eq 'git-init';

Note the $repo = "'$REPO_BASE/$repo.git'" line: it does contains single quotes.