No offense to your sister, but in most cases you can translate $ directly to CO2. If solar panels cost $10,000 then you could equivalently buy $10,000 worth of electricity generated by fossil fuels and the amount of CO2 released will be roughly the same. One always must remember that CO2 gets released as items are transported and manufactured, as the raw materials they require are mined, refined, and transported, and as the workers who make them go about their daily lives. (Example: even a painting can have a sizeable CO2 footprint, if the artist is a high-living jet-setter who spent a year producing it. The art lover who buys that painting is underwriting all of the artist's CO2 emissions for that year.)

Getting back to your sister: If the purchase and upkeep of the solar panels cost more money than the fuel she is not using would have cost, then she is probably doing the environment a disservice.

And there's yet another catch: Even supposing your sister does indeed save money (i.e., emit less CO2) in the long run by going solar, if she uses her savings to make CO2-emitting purchases that she would not otherwise have been able to make, then her net CO2 emission is unchanged.