Can the mother's mental state allow me custody over my children, even when not married?

I am a foreigner and have two children with a Filipina. I am not married and I am aware of the mother's rights, until the children are seven years of age. I am aware that under these circumstances, I have little rights. However, she already had a son with another man (he is 12) and she refused the father to see his son period. That son has been mentally and physically abused. In my presence, she hit him with a belt multiple times, recently she hit him with a coathanger multiple times where, according to her, she had to put him "in-line". Although my children are being cared for by her (i supply financial support), I am extremely concerned my children are being setup against me, will be mentally abused (if not physically) as they grow up. I had a high-profile psychologist involved last year and can have additional evidence from the family doctor about her behavior. Her narcissist behavior, her mental state are of deep concern (and well (well!!) recorded. Q1; Can this be legitimate reason for obtaining custody? Note; both my children have dual passports. Q2; Can I take my children overseas without her consent on their foreign passports?