There are two issues here, one being whether a letter is an appropriate genre and the other being Sara's actual situation.
Given the closeness of the familial relationship, this level of self-disclosure is appropriate. In general, it is not appropriate to share personal information with co-workers or strangers, but it is appropriate to share it with family or close friends. That being said, how people should best handle coming out to their parents really depends on cultural and personal context. In countries such as Saudi Arabia or Uganda, where homosexuality is illegal, the person might not want to inform his or her parents for fear of making them legally complicit.
In general, a letter is considered less intimate than an in-person discussion or telephone call but less superficial or casual than an email or text. While its limited level of interactivity can make it seem cold for an important child-parent communication, it does allow a level of careful thought and editing that can be useful in a fraught situation. If the person is on good terms with his or her parents, a visit might be more appropriate, but if the news could potentially be received badly, a letter followed by a visit or a phone call might be a good strategy.
Next, one needs to think of context. If the person lives in Canada or Sweden, and his or her two mothers are married, they would probably be delighted to learn of the relationship. If the parents are homophobic, sharing details of the relationship might not elicit a positive response. In the case of very elderly homophobic parents, discretion might be the better part of valor.