Custody determines who has the right to make decisions as the parent. Placement and residency determine when and where the child will spend his time. If you have shared custody, that means that both parents remain the legal decision makers of the child(ren). For major decisions, such as surgery, leaving the country, etc., both parents will have to agree. Primary residence does not grant the right to have final say or take away custodial rights from the other parent.
Primary residence or placement means that the child(ren) primarily live at one particular address with day to day decisions being made there, such as those regarding school, etc. In some cases (in some states), courts will order shared placement where the child(ren) is shared 50% with each household and does not have a primary residence, except for school purposes.
If mother has sole custody, then she does have final say. If she has shared custody, she does not and must consult you for major decisions. Primary placement will give her some authority over daily decisions.
If the mother of the child just has primary residence(or primary time-sharing as it is now called), this only means that the child stays with her for the majority of the time. Unless she also has sole parental responsibility, she is supposed to consult with you on major decisions affecting the child.
Your best bet is to consult with a family law attorney in your area to determine what your options are.
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