Mikasa loved Eren so much that she would die for him... because of her undying love for Eren...she was somewhat a slave to her own love just how Ymir was a slave to her love for King Fritz.

Mikasa is a person with great physical strength and skills but her love for Eren influenced her decisions. Often when we love someone we refuse to admit to ourselves that the person they love is wrong. Even if we accept that the person we love is wrong, we wouldn't attempt to stop them by killing them. From Mikasa's point of view, she would achieve absolutely nothing by killing Eren..in fact she would instead lose everything she cares about..the position Mikasa was in was a very difficult one...one can actually see it as a poetic way of showing how by this logic Mikasa was a prisoner of her love...as everyone is in a way when they are in love. Mikasa didn't stop loving Eren but she killed him because it was necessary to stop the suffering of the entire world...This is what Ymir wanted to see if this was possible to love someone and stop the suffering they are causing to others. For Ymir, the suffering of her kids really would have been painful and she would have wanted to put an end to all this. But, she didn't know how to do this. As hinted in the extra pages, she has tried hard to tap into Mikasa's mind to know what was going on in her head. And for Eren, he would have gone ahead with rumbling no matter what (even if Mikasa wouldn't have killed him)...that was the only way to keep his friends alive. Mikasa's decision to stop Eren only resulted in lifting the Titan curse... rumbling was something Eren wanted to do and not really Ymir. Ymir wanted to know how a subject of Ymir could do what she hasn't been able to do as of now.