So awesome and brave of you!! 
It was kinda similar situation in my case (but not really since I never studied abroad!) where my mom was the main one that was not up for me moving too far from home for college (bachelors). But yea - there was an untold assumption that I would apply anywhere I wanted when I went for my doctorate! Hence why I ended up in another state. Definitely eased my parents (specifically mom!) into this since now my siblings are having no problem applying anywhere and everywhere…including abroad!
… ahhhhh lucky younger siblings!