Based only on the facts you listed, you have a good shot, but the judge will consider many factors as well.
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The answer to your question depends on your definition of "custody". In Arizona there is parenting time and legal decision making authority (LDMA). LDMA deals with decisions in three (3) areas: health, religion, and education. Parenting time is what time the court awards each party to exercise time with the child/ren.
Given your circumstances/CPS involvement you have a strong argument for sole legal decision making and being the residential parent. The Court generally will still award her parenting time but it may be on a supervised basis depending on the CPS investigation. Good luck.
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