Courts strive to protect a parent's right to have contact and the possibility of a healthy relationship with a child, but even more so courts will protect a child whose safety is threatened or best interests are disregarded by a parent. His visitastion, if any, should be limited in time and heavily supervised by a paid professional (at his expense).
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You should discuss your situation with an attorney in your state knowledgeable in the law of child custody and visitation. The laws vary from state to state, but most states look at what is in the best interests of the child. This will involve a number of factors, including how well the child is doing in the custodial parent's custody, whether the custodial parent has impeded the other parent in having access to the child, and whether the non-custodial parent can provide a safe environment to the child for visitation. A lot would depend also on how long ago his transgressions which you list occurred, and what steps he has taken to become a better parent. Your daughter's age would also be factor. Judges like to ensure that children have relationships with both parents, and also of course that the child is safe and the relationship is healthy. Sometimes visitation in a situation such as you describe would start as supervised visitation for short periods of time. Each case is different, which is why it is important for you to consult with an attorney in your own jurisdiction regarding your own specific facts.
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He has rights to see his child, but the answer maybe "supervised visitation", he has a right to companionship with his child. My information suggests you should find a good domestic relations lawyer to minimize when and how he can see her.
My information suggests you have good facts on your side to potentially limit companionship and a good argument for supervised visitation.
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