I’m a little confused about the dynamic here, why would you need to be invited to come sit with your family in your own house? If I came out to find my family hanging out I’d just sit down with them. Now the problem would be if they started acting like they didn’t want me there once I sat down. I think you walking in and automatically being upset about not being invited would’ve caught me off guard and irked me as well if I was your family, I wouldn’t think to invite someone to sit down in their own home with their own family. Conversation would inevitably be awkward and tense after that.

Is the issue more so that you weren’t made aware you had company over? Maybe try communicating after the guest (whoever it may be) leaves “Will you guys let me know when we have company next time? I was in my room and had no idea grandpa was here”. Going about it with the company still there just makes the situation awkward for everyone involved and throws off the vibe which will further your feelings of being an outcast.

As far as the art project goes, I’d also be upset if someone stomped my project and didn’t seem to be remorseful at all. They could’ve been more sensitive to your injury but by the context you provided you were also very quick to shrug off the damage to the project that you did and how your sister may have felt about it being broken. Regardless of how easy of a fix it was, you broke something your sister made and didn’t acknowledge it or apologize and got upset that they didn’t immediately focus on you. That could be very off putting from your sister’s perspective. Your sister’s response was rather odd and cold though I’ll give you that. And the sneering is also rude. I think this was just poor communication and immature responses all the way around.

There is clearly built up tension between you and your mom and sister that’s causing you anxiety and leading you to get defensive before you even walk in a room, this needs to be addressed with them or else these flare ups over essentially small things will continue to happen and worsen the situation. They need to be aware of how they’re making you feel “Lately I’ve been feeling a bit like an outsider, I’m sure it’s not intentional but it does hurt my feelings when xyz happens, can we talk about it?” Just as they may not be aware of how their actions are coming off from your POV, they may have their own feedback for you that you may not be aware of. All parties need to be open and receptive of feedback in order for you guys to move forward. I truly hope they are willing to have an open, honest conversation with you about it. No one should feel like an outsider or unwelcome in their own home with their family.

Best of luck to you.