Might be better pausing university if i were you, you might be able to get it for free with the military as an officer, providing you pass course/selection. Also, seems a waste of your time doing a course if you really want to join the military.
Reference telling your family, i would start the conversation earlier if i were you. I was in the military for a good few years and come from a family who werent exactly pro forces. I think telling them over time helped eased things through, as they learnt about it as i did. You of course need to be ready for a good debate, but if it is what you truly want then they cant or wont stop you. I would highly recommend really getting to know the military as much as possible (speak to anyone you know is military etc, going to AFCO just to get info) will help make your mind clearer and will aid you having a good pool of knowledge if and when your parents push back. It shows them that you are are serious, and also how little they may actually know about it outside of the headlines. The military is not just a warfighting organisation, a lot of work involves keeping average people safe and ensuring international law is abided by (it gets a lot right and wrong of course, but the good rarely makes the news).
Good luck exploring the military,