I say this with an enormous amount of care and empathy and know this is sounds much more simple than it is, but the way you handle these situations is by handling yourself.

Stating you don’t do hugs, turning away and giving verbal niceties, whatever works for you is okay. You have to give yourself permission for that to be okay. You have to give yourself permission to not feel guilty for setting the boundary. Whatever emotion comes up for them is on them to manage, not you. Whatever emotion comes up for you is for you to handle, not them.

I know that sounds simple and it’s not, but if you’ve tried to say no, if your family doesn’t care, it’s time to work on your own response. It’s time to not cave in. It’s time to change the narrative you tell yourself when you set a boundary.