Is it ok if I want my sister to do the dishes?
Wow, that is shocking. Why should she do the dishes by herself?
We have some old glasses that need to be washed. She broke one of those once and she needs to learn how to handle them better
There is nothing wrong with splitting tasks among family members. While she washes the dishes, you could be cleaning elsewhere.
My sisters are never home and it's just not fair that I should do all the work.
Family members should always be fair in dealing with housework. Making one person do all of it is not going to work, share them and assign people to specific chores. Rotate the chores every week in case it gets to boring.