"przynieś dzieci" could be technically correct, but it would sound funny anyway)
Yes, in plural this might sound funny if the kids are kinda too big to be carried around. The expression, especially in singular, is often used for small children. For instance when a baby falls asleep we can say "przynieś dziecko".
So perhaps "przynieść" can be narrowed down to fetching of objects or persons in a way that their own mobility is not used and where English "carry" might also apply.
We can bring a full size donkey, but we can't carry it (him? :) - so it's "przyprowadzić"
We can bring a baby donkey, and it it can be carried - so "przynieść" will be just fine.
In short:
- if we bring something/someone by carrying using our own arms, hands, shoulders etc (but not vehicles) then it's "przynieść"
- if we bring something/someone by causing it to reach some destination with us (by leading, pushing, pulling etc) then "przyprowadzić" will be used.
- if we bring something/someone by first placing it in/on some sort of vehicle (car, coach, shopping cart etc) and then we bring the loaded vehicle along the "cargo" to some destination then then it's "przywieżć" in reference to the cargo. This is then a combination of the other two verbs.
Also, the above rules are not about just the ability to carry an object/person but about what actually happens. Therefore, the following would be perfectly correct: "Przyniosłem pijanego kolegę do domu" (I brought a drunk friend home) because he was so drunk he couldn't walk so I carried him. The situation described is unusual, funny (or sad) but the grammar is OK.