Multiple domains wrong urls

I have set up 2 languages with Polylang (free version) on 2 different domains, a .nl and .de domain. This all works fine until I pay or cancel an order.

What do you mean with 2 domains? Which URL you use to access your website homepages in NL and in DE?

Is this what you expect?
NL homepage -> http://www.my-website.nl
DE homepage -> http://www.my-website.de

The payment gateway you are trying to use is it paypal?

Polylang supports setting the language from the subdomain name in pretty permalinks, like this

NL -> http://nl.my-website.nl/my-post/
DE -> http://de.my-website.nl/my-post/

But I’m not aware if supports setting the language from different domains. You should check with the Polylang plugin owner.

In addition you will need to point both domains .nl and .de to point to the ip where wordpress is listening and configure some rewrite rules .htaccess file for that to work. I guess, you could eventually rewrite rules to map

http://www.my-website.nl -> nl.my-website.nl
http://www.my-website.de -> de.my-website.nl

something like before the wordpress rules:
RewriteEngine on
RewriteCond %{HTTP_HOST} ^my-website.nl
RewriteRule ^(.*)$ http://nl.my-website.nl/$1 [R=permanent,L]
RewriteCond %{HTTP_HOST} ^my-website.de
RewriteRule ^(.*)$ http://de.my-website.nl/$1 [R=permanent,L]

and configure polylang to set the language from the subdomain name in pretty permalinks.

In any case, this goes far beyond the scope of this plugin.