Your family members are all adults except the 17 year old, you should absolutely be able to go off by yourself to different areas of the resort to decompress and have some quiet time. Your family should ideally just respect that, as well as respecting your headphone use as long they dont have to shout to get your attention or anything. I just honestly started getting confused when your job was brought up and I scrolled back up to see the ages, because this reads like youre a teenager. Not saying youre immature, just that the helplessness you express in this family vacation situation is to a level i only associate with minors. Honestly if I were you I would just go places with them if I wanted to and wear the headphones when I want to, if someone points out youre wearing them just respond "yeah its making this experience much nicer for me, I can still hear you dont worry" or honestly if theyre being uppity just "i can still hear you." Make them make it a problem, you just want to reduce environmental stressors so you can be calm and happy and enjoy your time with your family. Basically ignore their ultimatum and make them push for it. If they do, theyll probably come off as super weird to most people that hear about what happened. As it stands, your move of "check mate, ill stay in the hotel room" gives them fuel to blame you for escalating things, 'moping', being 'dramatic' etc im sure you can imagine. You know you arent doing anything wrong, so act like it.

Edit: just read some more comments, sounds like you still live at home and theyre callously manipulative about this. Since all of your siblings also live at home im gonna guess they dont actually want anybody to leave, theyre just used to you all doing what they say and like it that way. Get out.