Sorry to hear what happened to your family. If your mum going to sell off the flat, though she is a first owner, as long the house has 2 owner, both need to sign. As for the contribution of the CPF, whatever amount both your parents contribute, after the flat sold, those amount will go back to their own cpf account.
Personally i felt you all need to settle everything with your dad first because if he kept finding fault with agent and buyer, your mum will not be able to sell the flat easily as these kind of info will spread one . I believe there must be a reason why your dad is acting that way. I do not know what actually happened but just put ourself in their shoe. If he has no job, no place to stay how on earth he is going to live the rest of his life? If your mum manage to sell the flat now, definitely will earn right. Then can give your dad some money to live on(Just a suggestion).
Sorry I cannot give much opinion, but if i were you, i would want them to settle down peacefully. Afterall, if they never ever love each other, how to have you right. Everyone has their reason being who they are now. is just we do not address what they want. I believe as long as you all can talk things out with your dad he will agree to settle down. Is there any reason why he has been jobless for many years? It must have been very tough for your mum. You can do it as long as you have to believe in yourself. God bless. Please take care okie.