Translatable Child-theme: same or different textdomain

Hi,
for a website in Polish language, to customise the templates and allow for updates of the base theme, i decided to create a child theme.
I was seeking for any complete howto or article concerning the strategy: I am using poedit to create translation files, and Codestyling localization to keep them up to date, but I cannot get those texts to display on the site internationalised with Polylang.

I am trying to create a textdomain separate from base theme (brunelleschi), but the Codestyling Localization still displays the ‘brunelleschi’ textdomain.

Here the code of functions.php of my child theme, “Andrea Brunelleschi”, where I’m overriding the function brunelleschi_setup() of main theme.
Any hints are welcome.

[Code moderated as per the Forum Rules. Please use the pastebin]

And some template file:

<h1 class="page-title"><?php
				printf( __( '%s offered by MyCompany', 'andreabrunelleschi' ), '<span>' . single_cat_title( '', false ) . '</span>' );
			?></h1>

Thanks in advance.