In 1998, the UK restricted sales of paracetamol (acetaminophen) to packs of no more than 32 tablets. The result was a lasting reduction in suicides by paracetamol poisoning, with no commensurate increase in suicide attempts by other means. Several studies have found that interventions like installing suicide prevention barriers on bridges can reduce the suicide rate rather than merely changing the choice of means.
https://www.bmj.com/content/346/bmj.f403
https://www.hsph.harvard.edu/means-matter/useful-links/bibli...
If you take an overdose of tablets or slit your wrists, you'll probably survive with suitable medical care. You probably have the opportunity to change your mind, call an ambulance and save your own life. Very few people survive a gunshot wound to the head; all of them sustain life-altering injuries.
You have the right to own a gun, but that comes with responsibilities. You need to recognise that your gun poses a serious risk to you and your family, especially if it isn't consistently stored in a suitable gun safe or someone in the house is at risk of suicide.
If you're worried about the mental health of a family member, controlling their access to convenient and highly lethal means of suicide could well prevent an impulsive decision from becoming a tragedy. Clear out your liquor cabinet, throw out any surplus medication and get your gun out of the house.
https://www.vox.com/2015/7/30/9068255/suicide-impulsive-gun-...
There are so many ways to commit suicide it's hardly worth listing them here. If her family kept any pills in the bathroom it's likely she could have killed herself without leaving the room.