The S3is was/is a fine little camera(I had two..!)- but in one or two areas would be lacking by today's standards.
Your daughters Softball playing highlights those very shortcomings- that being poor noise control past iso 200(necessary for moving subjects if light is less than ideal),a lack of a decent burst mode(though was one of the better ones back n the day),and lens fringing issues.
There are no "add on's" that will address these shortcomings- and you would indeed be best served by an upgrade- though I'd keep the S3is as a back up- as it's still a decent all rounder,with its great image stabiliser,surprisingly good video mode,swift autofocus and generally sharp lens.
The latest candidates for a "bridge" camera would be-
Nikon P500(5100 due out)
Sony HX100v(200v due out)
Fujifilm HS20(30 due out soon)
Fuji XS1(if budget allows).
I own an SX40HS and am quite happy with it- though if outdoor sports are your bag- maybe consider the Panny' FZ-150 with its class leading autofocus speed and very fast burst mode.
Here's a few "sporty" shots taken with my SX40HS...