Assuming you crop to the same area and print to the same size, the amount of camera-movement blur should be indistinguishable between the two cases. Using a shorter focal length will decrease the impact by exactly the amount you have to crop and zoom.

So, it comes down to other factors. The most important (from the narrow viewpoint of camera-shake blur) may be that your zoom lens may allow a wider aperture at shorter focal lengths, which would let you speed up the shutter, reducing blur.

But in real use, I don't think that's necessarily going to make up for the decrease in resolution.

I think what I'd do is ask the kids to let you take turns taking pictures and holding them. They'll appreciate looking at the pictures, too.

Assuming you crop to the same area and print to the same size, the amount of camera-movement blur should be indistinguishable between the two cases. Using a shorter focal length will decrease the impact by exactly the amount you have to crop and enlarge.

So, it comes down to other factors. The most important (from the narrow viewpoint of camera-shake blur) may be that your zoom lens may allow a wider aperture at shorter focal lengths, which would let you speed up the shutter, reducing blur.

But in real use, I don't think that's necessarily going to make up for the decrease in resolution.

I think what I'd do is ask the kids to let you take turns taking pictures and holding them. They'll appreciate looking at the pictures, too.