C.S.
By law you have to use the Private ins first , the govt (Mediciad ) second. You don't get to pick and choose which one to use ! You may also want to contact the private Ins and tell them he has a govt Mediciad program second, so there won't be a problem later ,when they receive claims. You don't necessarily have to give up the Mediciad ,but , you should also make Mediciad aware of the other Ins.
C. S.