I am not certain but I'm pretty sure you can get data about the texts like time stamps, who they were to and from, and even which towers they were sent and received from but not the content of the texts. I'm not 100% on that though.
Whatever you can get will require a subpoena. Even if the phone is part of a family plan if it is not your phone you can't get the data. Even getting the records from the phone of your own minor children requires a subpoena. If the cell companies don't keep a copy of the text body, which I'm pretty sure is the case, they can't give that over even with a subpoena, just the metadata.