If you allow the relationship to continue you can push back hard and demand better, or adjust your expectations so that her behavior does not affect you so deeply. Both options have pros and cons.

As for cutting someone out, that is a very difficult road. You'll always wonder what would be if you had stayed in the relationship and you'll always feel a void. It is very difficult for other family members as well. Sometimes this is the best way given the alternatives.

An alternative would be to let your sister know you need a break. Explain to her that her behavior is undesirable and that you need time away to get perspective.

If you go either of the routes that pushes her away for some time, try to do it with grace and mercy. Tearing her down on the way out won't serve anyone and a peaceful exit makes it easier to come back together in the future in the event things change.

It is incredibly difficult to know which decision is best. I would sit with each option for a day or so and imagine it were true. If it feels wrong, it's wrong. If you can live with it, it may be a viable option.

I wish you the best with this. I know personally how difficult this can be.