What a terrible thing you had to do...very good of you to have the strength to do what's best for your baby, even though it wasn't the easiest for you.
Having raised quite a few chicks and also having three full grown cats (and 2 dogs) I would like to step up to the defense of the bad cat...cats do what their nature dictates, which is to hunt and take down those that are (usually) smaller and defenseless, including mice, baby bunnies, pretty songbirds, frogs, and of course, chicks that they are able to get to. Just their instinct. I hate that particular trait, don't get me wrong, but they aren't "bad" for doing what they are able to do.
We have raised at least 75 chicks from day old to fully feathered (and I know we are by no means experts, nor is that a lot of birds to others here) over the past four years without incident and with our three indoor/outdoor cats right there--and our cats can and do take down all of the little creatures they are able...I wouldn't just re-home the cat based on this sad incident, unless it was just a cat who already had a bad 'cattitude' to begin with!
Also, your chickens will also 'kill other animals' given the opportunity..I've watched mine take down a meadow vole and a couple of toads and frogs (and I tried to save them but the girls were just too fast!), not to mention the myriad of bugs they so enjoy to munch on...
PS: Once your chicks are grown up it's unlikely your cat would bother them...my chickens have chased at and pecked my cats, and even my Aussie who was just trying to get her ball, which had rolled close to our Buckeye, Patty...Patty wouldn't allow the dog near the ball.