Everyone is saying that your family member did something illegal...I'm not entirely sure that's the case. According to HIPPA (the US Healthcare privacy laws), only protected health information is covered. From the website, this includes
“Individually identifiable health information” is information, including demographic data, that relates to:
the individual’s past, present or future physical or mental health or condition,
the provision of health care to the individual,
or the past, present, or future payment for the provision of health care to the individual,
and that identifies the individual or for which there is a reasonable basis to believe it can be used to identify the individual. Individually identifiable health information includes many common identifiers (e.g., name, address, birth date, Social Security Number).
However, your family member didn't disclose any of those things...she told your mother that she saw your gf at the abortion clinic where she works. Yes, she could have been getting an abortion. Or she could have been there for a friend. If your family member looked at the patient info, saw she was having an abortion, and shared THAT information, then that would be wrong. But if she just said she saw someone there, I don't think that's protected information.
If that's the case, then if one of your friends was also in the waiting room and saw your girlfriend there, would it be illegal for them to tell you they saw her there? Of course not. Disclosing someone's presence at a certain location is not the same as disclosing their private healthcare information.
If your girlfriend was there for herself, and did have an abortion without your knowledge, that would be a dealbreaker for me. It reeks of distrust (because she doesn't trust you to support her) and selfishness (because she wanted an abortion no matter what, so she circumvented any situation where you might have opined otherwise), as well as a disregard for your feelings in a very sensitive relationship issue. The abortion itself is not really a big deal...the fact that she left you out of the loop completely would be a BIG relationship red flag for me.
And yes, I do think cheating is a possibility, especially if you two use condoms as your main form of birth control.