Check if we're the second or last sunday of the month today
Maybe it doesn't work because the monthyear variable is formed in dutch and not english? 


Yes that's part of the problem. Have a look at PHP's relative formats page to see what it supports. 

You can actually pull off what you're doing with the this keyword.

{% set secondSunday = now|date_modify("second sunday of this month")%}
{% set lastSunday = now|date_modify("last sunday of this month") %}


You also don't need to define (or override) now since Craft will always set that to a DateTime object for you.