Husband left me with our daughter just turning 3

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Two months ago, my husband told me that he doesn't love me anymore...( I am a FIlipino and my husband too, our culture is very conservative, especially on marriage and family matters) Yes I had faults, many faults, I thought that his love was enough to accept me for who I am, or so I thought, only to find out that he is somewhat living in with another woman... He just show up every Sunday to go to church and eat out, that's his means of spending time with my daughter. He resents being with me but I can't allow my daughter to be alone with him... I don't know if I should continue to allow this to happen or just totally get him out of the picture and raise my daughter alone. He said he's never coming back to me and at one point he told me that I can tell my daughter that he is already dead... that's how he hates me...Can I just take him out of the picture just like that just like how he wants me out of his life? His parents knows none of these, he said he's just in a boarding house thinking and evaluating himself...