Well, grammatically it should be (1) because 'get' (as in cause to) + noun requires an infinitive (to-form) and not a gerund (ing-form). I think the difference is that in (1) you get the kids to do the cooking as an activity they do themselves, while in (2) you want to get, as in retrieve, 'kids cooking' -- sort of as one word. ) requires the infinitive.
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