"Get someone into something" can have several meanings, depending on the context.
In this case, an accurate reading might be "make sure that she starts rehabilitation." This could be a program or it could be a literal center. You're right that "get her into rehab" makes it sound like they might be referring to an actual rehabilitation center with a building she can go inside.
Sometimes "get someone into something" means to make the person interested in something, usually referring to a hobby or a TV show or an interest. Here, rehabilitation isn't really a fun hobby or interest, so this is probably not the best meaning. "Get her into rehab" is quite a strong way to suggest (or even command) someone to make their daughter go to rehab, so this phrasing was probably chosen to convey urgency ("If you possibly can, get her into rehab as soon as possible).