Imagine this, you're a teenager, at the spring of your life where you have near the amount of rights an adult have and none of the responsibilities, you should be enjoying the time of your life as you will not be able to again once you reach adulthood, yet you can't, all because your brother wants to live the way he wants without regard for his family and you have to keep everything together.
By no means am i saying mogumo is wrong, if your family rejects your very being because it does not allign with their values, it's natural that you would avoid them. But it's understandable that his sister came to hate mogumo to the point of wanting to throw up from acting nice to them, from her point of view mogumo is the selfish older brother which is the root of all of her problem. Mogumo's out there enjoying life, dealing with the woes and trials of adolescence while sakura is stuck having to deal with things that aren't supposed to be her problems.