IMO, IF Julia did in fact send her son into hiding, it wasn't to protect him. She would've done so out of spite. Obviously, JB knows that her accusations against Solomon are false because she preferred Solomon be given custody of M rather than having her sent into foster care. But, she repeatedly made false allegations against Solomon to keep the children from him in the past, and he just regained visitation rights prior to the staged abduction.
Why would she hide one child and not the other? Especially in the middle of custody negotiations. She had to know what that would do to her custody rights on her daughter. I don't think that idea has any legs.