Taking photos of my active daughter

I currently have the Canon PowerShot SD960.  I like it but I've dropped it a few too many times so it's time for an upgrade.  I mostly take pictures of my daughter, who never sits still and I have to be on the ready any moment to capture her!  Since my daughter is always running around, I often take pics  of her at a distance and then crop them on my computer later to get a close up.  Zoom of the 520 sounds cool, but I don't like the things I'm hearing about "noise" and poor battery life.   I don't think I'd have time to zoom sometimes with her.  With my SD960, I'm already changing out my battery every outing b/c I take so many pictures.  I also like to take short HD videos.

I was leaning towards the ELPH 110 from the beginning, but friends are trying to convince me to get the zoom of the ELPH 520.  I'd love some good advice!  If the ELPH 110 is just as good as my SD960, I'd be satisfied with that.