Hello @belay,
We apologize for the delayed response.
Regarding your query, while we have tested the WP Travel Plugin with Polylang the custom post types added by the WP Travel plugin are available for translation with Polylang.
While there are available options ( like displaying the archives with itineraries shortcode ) already available with the plugin, it should be listing the archives by default with the use of polylang.
To debug the issue further, please check by creating a translation of any trips in the backend and check if the dashboard language switch and default ( starred language ) settings are all correct in the polylang settings.
If the issue is not resolved, please provide us your website URL so that we can check the issue further.
Best Regards !!