Yes/No, Moving Out, No Separation Agreement

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You can move out, and I strongly suggest you get a domestic violence protective order against her as well.
I suggest you file for custody immediately after you move out.

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You need to go to the courthouse in your county and speak to the clerk of civil court, who can provide you with instructions on how to obtain the protective order.
The order could negatively impact her job, but I cannot say for sure what impact, if any it will have, it depends on her specific employer.