Custody and visitation are determined by what is in the best interest of the child. If the father is suicidal and considered to be a danger to the child, that will certainly have an affect on the case. You should contact a child custody attorney in your area to help you with your case. They will be able to explain and apply the statutes and case law governing the "best interest" standard.
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They would help you out tremendously. Your attorney may be able to build a case for supervised visitation only, until these issues are under control. The best interests of the child will be protected.