I'll add that OP & spouse won't be able to watch her constantly, either. Maybe for a few days, but not long-term...
That is why she should be STRONGLY encouraged to participate in an on campus educational program and get a job outside the house where she can be observed for problems arriving from depression and her apparent health issues (from the insulin references). Often talking will not work; other means - including withdrawing financial support - may be necessary. OP needs to try all means necessary to get the child into an appropriate environment - not necessarily living at home.
The stigma of mental illness is such that the individual, family and friends want to deny it exists. It frequently appears in the late teens and 20s. A person who has made one suicide attempt has a serious problem and to be dismissed as not being mentally ill becaust they failed is foolish. Why risk other attempts when the chance of success increases with each try. There is much online from reputable sources regarding severe mental illness among young people.
Unfortunately, someone cannot be institutionalized for what they might do. In patient care is short term. The best that can be hoped for is to have ongoing care - even when the person seems to be doing fine - and encourage them to be in a supportive environment. It takes a different type of "tough love" to deal with someone who has made an attempt at suicide.
As the parent of a mentally ill adult child who has dealt with issues of suicide prevention, hospitalizations, medication, appropriate psychiatric and psychological care, ... for over 20 years, I am qualified to speak to anothe parent just beginning the journey. OP's child's life depends on the entire family being honest, informed, supportive and proactive.