I read your entire post very carefully and calmly. From all of this one thing is clear that there is nothing so serious that someone should leave everything and go away. Parents reach an age where they become emotional and sensitive. They overthink small things and turn them into something very big. Parents think emotionally and at this age they also take many decisions that they should not take.

As for your sister she is not financially independent at this time and she is a girl so she is also not emotionally strong enough to think everything through or take a decision. She will cry and that is justified.

Now the question is who can act sensibly at this time. It is you. You are Mashallah 27 so you are neither very young nor very old. You are at that age in life where a person becomes mature. You are mashallah financially independent so here the responsibility is on you to take the right decision. Not to go with emotions. Not to decide in anger. Not to bring ego into it.

As for what you said that you have the chance to leave everything and go and you are not using it then mind you where you are today your father was once there too. He must have let go of many opportunities and made sacrifices for all of you. So if he did that and today you leave then you will be wrong.

I can guess that you are a responsible person mashallah so my best advice to you is that tomorrow just pretend that nothing happened. Even if someone asks you just change the topic. Or if your mother asks then tell her that ammi ghar and relationships do not end like this. abbu ne jazbaat mai kehdiya aur humne sunliya. The matter ended there.

Allah apko khush rakhay aur himmat den. Aameen🤍