Ok, I've tested a lot with different ways to build the translations.
I only use the .xlf files. But how to build them and where to place them.
In the manual I read /translations/nl-NL/Module.Mymodule.admin.nl-NL.xlf
I installed my module and went to International - Translate.
Then I exported the translation and downloaded the file ModuleMymoduleAdmin.nl-NL.xlf.
I had to copy its contents to Module.Mymodule.Admin.nl-NL.xlf . However, this file must be located in /translations/ and not in /translations/nl-NL/
After each action, I cleared the cache, either via PrestaShop or FTP.
This seemed to work fine. However, I still have the problem that the module manager doesn't change the language of my module when I change the language of the back-office.
So I'm still looking for a solution for that.