As Phillip told you: "So my conclusion for next time is that even it is in the middle of the night and they come with small kids, don't let them in the apartment in the first place. To get them out or to get refunded is nearly impossible." [i.e you will spin around and wont be able to solve much now]
This might not be what you want to hear...or even sounds appeasement; but Saskia even living close by you allowed this to happen and now are faced with a fait accompli [sic]
1. On one hand people acting this way, as a rule as not most trusted sort or to base anything on them [future wise]
2. On the other, exactly these types, will 'make things up' and as as result you will be fighting on many fronts with Airbnb, [asking for extra money, then justifying 'wrongs' the guests might accuse you.
What gives.
If it was me, I 'would let it go' But in a FIRM WAY, tell them in no uncertain terms [fight part] what they did wrong, and say it LIKE YOU MEAN IT. Then, offer some leniency [peace] and 'for sake of little children' will allow them to stay THIS TIME. [you might start wanting more money and end up losing Superhost status and few other troubles]
If they are good, bake them some biscuits the day the leave [be around at that time and v. visible near by] if they are a mess...then escalate as much as you can..and see when it ends. However you see it and it ends, dont blame Self; it happens.