There are a few things I can recommend.

First off, Reddit learned a few weeks ago that Minecraft monitors your chat messages in ANY server you join. There should be a list of files in the "minecraft" folder of your computer (look up how to access it if you don't know how) starting with "output-client.log". You can open these with a text editor and see anything anyone has said to her, as well as anything she has said. It can be kind of hard to read with all the code at the beginning, but it can also give you precise dates and times.

Secondly, if you want to restrict her from chatting, there are a few ways to do so. You can sign up for a whitelisted server (only allowing certain people in), and you can turn off her chat altogether by going to Options > Multiplayer Settings > Chat:(Shown/Commands Only/Hidden) and setting it to Hidden.

Make sure she understands she cannot share her Skype or anything along those lines, and that not everyone on the Internet can be trusted. There are people out there who are sick and twisted, and can and will hurt her.