Hello. I believe I can be of help to you with this issue.
I'm glad that firm limits have been set regarding the PRIVILEGE your granddaughter has been granted to be on Face book, a phone, and computer access. I would continue to talk to her about the kinds of behavior specifically, that will allow her to EARN BACK the privileges. It isn't clear in reading your post whether you implemented the limits or her mom did
. The key thing her mother needs to be doing is to continue to maintain these consequences, but at the same time, try to engage her daughter in conversation about expected behavior and some form of restitution. So for instance, if she is grounded, what can she do to get ungrounded e.g., specific series of chores or work-help around the house, or perhaps compose an essay about problems some teens get into when they go on line, etc.
I don't know what taking her to the doctor would do. If she is truly suicidal or talks of specific plans, she should be taken to the emergency room of the hospital and checked in for an inpatient stay and observation. However, if she is simply very angry and is actively protesting the punishment and the communication between her mom and her has broken down, an offer to talk to a family counselor together might help. Her mom can try to convince her that going to the family counselor TOGETHER to help improve communication and reach new agreements about expected behaviors will get her privileges back sooner.
I'm going to pause here and solicit your feedback. I'm very concerned that this girl may not have a healthy, supportive strong paternal (fatherly) influence in her life (?)