"Children's Magic" is generally considered to basically be a dedicated branch of magic, because as you've encountered, you can't use your normal approach.
There's lots of info out there much better than I could possibly give, but I'll try to convey the basics for you! There's a pretty standard lineup of proven material when it comes to performing to children (Magic Coloringbook, Spongeball routines, Lots of vanishes and reveals, etc). But if you're interested in straying from the beaten path, then it's important to realize the common themes behind these tricks.
The biggest one is that all the tricks are very very visual. When performing for older spectators, I personally prefer a very cerebral presentation, I like to deceive the mind rather than the eye. However with kids, usually you want to do the opposite. Even if someone is not paying attention, if they catch something disappear, or change colors, out of the corner of their eye, they'll be impressed/surprised/whatever. So that's a method by which you can keep their attention, because it only requires a small amount of it (compared to something like ACR or something where you have to follow it pretty closely)
Another theme is usually how quick a trick is. For children, you don't want something that's long and drawn out, because even kids with good attention spans still get bored at superhuman rates! So try to do self-contained tricks, instead of long routines.
And possibly the most important is to do tricks that the kids can interact with. You'd be surprised how often you take the most distracted, loud, obnoxious kid in the room, select him as the volunteer, and he becomes your biggest fan! Kids love when the magic happens in their hands, or "because of" them, or responds to their suggestions.
Those are just a few generic tips, hope it's a bit helpful!