Ah, I see the problem now - should have waited to reply.
The problem is the newlines in the source around the "widget-ko_calendar--1-widget_events" tag. The code I posted above is designed to remove the first, and only, child of that tag, but there are 3 children. The newline right after the <div> tag and the newline after the next <div> tag. So the first child is the newline, not the "loading icon".
<div class="ko-calendar-widget-events" id="widget-ko_calendar--1-widget_events">
<div class="ko-calendar-widget-loading"><img class="ko-calendar-widget-image" src="http://dev.jesuschurch.no/wp-content/plugins/google-calendar-widget/loading.gif" alt="Loading..."/></div>
</div>
I suspect that replacing the code above with the code below will fix the problem. How are you generating that code? I guess I never noticed this because it is all generated by the plugin - but you say that you are doing it manually, so that might be the difference.
<div class="ko-calendar-widget-events" id="widget-ko_calendar--1-widget_events"><div class="ko-calendar-widget-loading"><img class="ko-calendar-widget-image" src="http://dev.jesuschurch.no/wp-content/plugins/google-calendar-widget/loading.gif" alt="Loading..."/></div></div>
As for a proper solution, I should fix that script so that it can handle white space around the <div> tags. Can you try the fix above and let me know if it works, I will hopefully get around to fixing the script up as well.