Hello Josh
My name is Nigel and I'm the second tier supporter in Toolset. Let me interact with you directly rather than via Mateus, as this thread has already passed through several hands is already somewhat confused. (This is understandable, because how Views and templates are translated changed with the introduction of Blocks and the View block, and the documentation linked to earlier assumes you are using the Blocks editor, but you are using the legacy editor for Views and templates.)
I have been looking at your site but I haven't been able to get very far analysing the problem.
On your site the default language is English, and you have German as a secondary language.
But when you describe the templates and Views which you set up to work with these modals, you talk about the German versions.
However, in the back end when you go to Toolset > Content Templates or Toolset > Views, it only lists the English templates and Views. The German versions cannot be accessed.
That is partly by design (but also reflects a design flaw).
Typically, it was not required, nor expected that you translate Views or templates themselves.
Clearly the texts output by a View or template would need translating, but the View or template itself would not be translated.
If you added a View (via shortcode) to a page and translated the page (retaining the same shortcode), on the front end when you switched to the second language the WPML would modify the View query so that it returned results in the intended language. In the output of the View, where you had dynamic content—e.g. you output the post title using the wpv-post-title shortcode, or custom fields using shortcodes—this would automatically retrieve the correct language version of the text to be displayed.
Static texts—e.g. if you included an H3 heading with some static text—could be handled by wrapping the texts within wpml-string shortcodes, and then locating and translating those texts with WPML String Translation.
So all of the texts output by the View or template would be generated in the appropriate language, even though the same View or template was being used with each language, without translating the View or template directly.
It was, nevertheless possible to translate Content Templates, for the scenario where you wanted the design of the page (and not just the page texts) to be different in different languages.
The design flaw I referred to earlier is that you can only translate Content Templates with the WPML translation editor, it is not possible to edit a different language version of the template in the WordPress editor (whether you use the Classic editor or the Block editor), as there is no language switcher in the admin toolbar to switch to another language when listing the available templates, nor is the WPML UI available to set language and choose editor available when editing templates in the default language. (I see we have some internal developer tickets about this issue which have gone stale; I am going to push for them to be handled soon.)
In your scenario, whereby you have a template that includes Views which between them are responsible for outputting a modal, I would expect these to have been created in the default language and to not have been translated themselves, but for texts generated by the Views and templates to be translated as I described above.
And in that case I would expect the functionality around modals to work in whatever language the page was being visited in.
But right now we have a scenario where you have some English Views and some German Views and some English templates and some German templates, though because the default language is English and because there is no language switcher available when listing Views or templates, it is not possible to open the German Views or templates in the editor. It is—I understand—the German versions which are working, and the English which are not, which is unfortunate, given that English is the default site language.
I wonder if you have been able to edit in both languages by switching the default language while editing?
In terms of how to resolve this, it implies work, but my instinct is to decide categorically which is the default language for the site and stick with that, recreate the Views and templates in that language as necessary, then delete any Views or templates which are in the other language. (I would likely need to help you with that.) Set both Views and templates as not translatable. Then translate any outstanding texts via string translation, as described above.
Let me know your thoughts.