The mother of my daughter is threatening me with 2 hour supervised custody and threatening to move her out of the country all because I have a new partner and baby. We are separated and never married but I am on the birth certificate. She has stopped me having my daughter over night and will not even let me have her near my partner, even though we are both neither any threat to her. Are there any laws that can help me stop her taking her out of the country and do courts only allow 2 hour visitaion rights?

Yes, it is called a court custody order.

So when you went to court to get court ordered visits, have court ordered child support ordered, what does that order say.

Without a court order, she can do what she wants.

The mother of my daughter is threatening me with 2 hour supervised custody and threatening to move her out of the country all because i have a new partner and baby. We are seperated and never married but i am on the birth certificate. She has stopped me having my daughter over night and will not even let me have her near my partner, even though we are both neither any threat to her. Are there any laws that can help me stop her taking her out of the country and do courts only allow 2 hour visitaion rights?

You need to file an action immediately to establish custody and visitation. That will also require you file an action to establish your paternity and the custody and visitation orders will be brought as part of that case.

In California you are given automatic temporary restraining orders (called ATROs) as a result of filing your case and they enjoin you and the mom from removing the child from the state without the other's written permission or a court order. Check with local counsel in your state to see if your law provides for automatic orders like these going into effect as a result of opening a case to establish paternity and obtain custody orders.

A threat of removing the child from the country is serious and could amount to parental kidnapping (a crime) if the child's mom does this. Additionally, the mere threat of doing this could be grounds for you too seek an emergency order granting you custody(at least temporarily). Don't put up with this nonsense and don't be intimidated by your co-parent's threats of placing you on supervised two hour visitation. Supervised visitation is for people with serious parenting problems (drug/alcohol abuse, domestic violence). That you have a new partner and baby is none of your co-parent's business and is irrelevant to this case.