I don't mind if their father has visitation rights but i don't want them to be able to stay the night.
In general, there are two ways to "get custody" of your child. One is to file a lawsuit in the jurisdiction you and the child reside in. You and the father then may have an order entered setting out the rights of you both. Some jurisdictions have mandatory mediation programs that you must attend once a lawsuit for custody is filed.
Two, you may enter a parenting agreement that sets out the rights and responsibilities of you both, along with a parenting and visitation schedule.
Certainly, a local attorney in your area could assist you with answering questions and determining whether or not your jurisdiction has mandatory mediation. If your jurisdiction does not have mandatory mediation, you are also free to voluntarily mediate your case, and enter a court ordered agreement from that. Some lawyers are certified mediators and could assist you and the father in coming to an agreement relating the the rights referenced herein. Again, a lawyer will be needed to draft that up for you. While the advice from the other attorney answering this question is correct, what you want or mind is irrelevant, certainly, if you have a hearing, you are able to inform the judge what you think is in the best interest of the child, and what arrangement you prefer or do not object to. The judge is then free to use your input, along with all the other evidence and testimony in the case, to make his own decision about what is in the best interest of the child.
There's just one step - hire an experienced family law attorney that you are comfortable with and that quotes you a reasonable fee. This may not be the answer you were looking for but it is likely the best answer for you because right off the bat it appears you will likely not be able to do this yourself because you seem to think the Court cares about what you do or don't mind or what you want. When it comes to custody, North Carolina judges generally use one standard to make their decision - what's in the best interest of the child. What you mind and what you want are irrelevant.
DISCLAIMER: This answer is for informational purposes only. It is not, nor is it intended to be, legal advice. Merely reading our posted answer does not create an attorney-client relationship. You will need to formally retain us by signing a Professional Services Agreement and / or making payment of a quoted fee in order to be considered a client.
The determination of custody is decided based upon the "best interest test" meaning what is best for the child. Generally it is hard to cut off contact with one parent unless there is proof of abuse or substantial harm or risk to the child.
The statutes presume that joint custody should be granted until findings are made to show the same would not be in the childs best interest. Most of the studies show that children do better when having frequent contact with both parents.
I would need more information about the circumstances before being able to offer more detailed advice
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