What is the Shar'i (Islamic legal) ruling on keeping a previous marriage a secret due to consummation and threats of suicide, and is it preferable to inform the divorced wife's family about the situation, especially given the father's illness and the family's refusal to allow the husband's return?

The girl becomes a wife simply by virtue of the marriage contract, and whatever is permissible for a man from his wife becomes permissible for him from her. Upon consummation, she becomes entitled to the full dowry. There is no sin upon them for what happened, but it would have been better to observe custom. Her family should not be informed of what occurred if it will lead to something undesirable, and you must acknowledge having consummated the marriage with her if she needs that to clear her of any accusation. You should seek another woman as long as her family does not approve of you.