One of the first words that came to my mind was rugrat (sometimes written as rug rat). Many dictionaries I checked (including Dictionary.com, Macmillan, TFD, and the Online Slang Dictionary) indicated the word is
- used to reference young children
- chiefly used in North America
- often used humorously or affectionately
It doesn't particularly denote mischievous children, although the term does seem to convey the notion that such young children are mischievous in general.
Another more general term would be brat. Macmillan indicates this word could be considered insulting:
brat (n., informal) an annoying child who behaves badly; an insulting word for a child
but Collins allows for a more playful usage of the word:
brat (n.) a child, esp one who is ill-mannered or unruly: used contemptuously or playfully
Whether brat would be considered derisive or affectionate would depend largely on the tone in which it was used, along with the facial expressions of the person using the word. One could use it in the context you describe in your question, especially if the word was uttered more good-naturedly than harsh.
I'll bet there are plenty of other words that could be used. When I looked for synonyms of brat, I stumbled across whippersnapper, which Macmillan (correctly, in my mind) labels as old-fashioned. Yet it's still a valid candidate; when dealing with kids, you might prefer to not use the same term over and over again without mixing things up on occasion.