Hey again quixote888: 
Have you thought about getting some counseling for yourself? Perhaps you could bring your wife to a session and discuss your cousin's suicide together, with a therapist.
It would be a good idea to make a Safety Plan, in regard to your wife and possible future suicide threats. It might help reduce your stress level, if you can feel more confident regarding how you will handle situations with your wife, in regard to suicide ideation. The link below can inform you about safety plans.
SAFETY FIRSTI don't know if you are in the US or International, but one of the links below could be helpful for you. You might want to reach out to a suicide prevention hotline. Part of their service is to help family members of those who struggle with thoughts of suicide. You could connect with someone on one of the hotlines and discuss how to inform your wife. Talking to someone on the phone about your situation could be beneficial. The first two Resources below are for the US and the third one is for International Resources.
SUICIDE PREVENTIONTEXT CRISIS LINEINTERNATIONAL SUICIDE RESOURCESYou might want to check out the information at the links below. The first one is in regard to "Suicide Ideation in Others". The other two, might not apply to you, but you might want to read them for future reference. Some people encounter situations where a BPD partner will make threats of suicide as a form of manipulation (emotional abuse). You certainly want to take threats of suicide seriously, and it can be part of your safety plan to get help from professionals and not let your partner use suicide threats as a form of manipulation.
SUICIDE IDEATION IN OTHERSWHEN YOU ARE MANIPULATED BY SUICIDE THREATS WHEN SOMEONE THREATENS SUICIDE What do you think about some counseling for yourself? Sounds like your wife uses alcohol to self-sooth. Has she ever been successful with using some healthy means to self-sooth?