Why would she be responsible for stopping her sister? It's her sibling, not her child. Also, she did try to get her engaged to someone else. The sister still forced her way into being a consort. Even now, MC is trying to stay in contact with the man he wanted to be his sister's fiance.
Just blame the parents. The MC asked the parents to stop the sister and they refused. They are also the ones who spoiled the sister while putting excessive expectations on MC. At this point, I only blame the sister about 20% and blame the rest on the parents.

Warning spoilers:
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I know understand why MC is stuck in this re-birthing loop. MC knows what’s going to happen (ultimate outcome: death for all) but didn’t fight against her sister entering the palace. She even allows her naive sister to step all over her. Make it make sense. If you were in her situation, you would do whatever it takes to keep your sister out of the imperial politics. Mc knows that being weak/soft now would cause their deaths eventually and she still doesn’t remain firm with her sister. Her problems are valid no doubt but her character flaw is quite serious. No wonder she is stuck in this vicious loop of re-birthing because she keeps making mistakes that are within her control.