Failing on the Samsung S3. As I understand the specs the S3 does not have the IR blaster.
However, if that is incorrect with respect to your particular phone then the issue may be the control codes involved.
Do you have the IR code for the Pace RNG110? I found 01982, IR is 38KHz. However Charter Comm may be using some other values for its cable box version.
Did you try the IR extender on the Pace RNG110? Saw that as a possible fix on one website.