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.