Responses
I think it's more likely her half-sister want to marry him and ask her dad for marriage that's why she want to kill the FL because she knows that the Rutger won't divorce her. (This is just based on future Rutger expression so eh)
Past Rutger probably didn't know how to properly communicate to mc at all because of all the abuse he went through so even if he did love mc he didn't know how to act it out. But at least he didn't seem like a bad person towards mc. Sure he never communicated with her, even during sex, but he treated her with a level of respect by waiting until she is ready before their first night together. Only thing that confused me was the promise between mc's half sis saying she was promised to be Rutger's wife or something. But I assume Rutger was lying and will back stab them after they helped him with the rebellion?
Mc's actions of pushing child Rutger away seems realistic and valid as it reminds her of her panick when she returned back to her original timeline, as well as looking at a young version of ML will give her thoughts of "this could've been what our child would've looked like". There was also the thoughts of ML possibly betraying mc and being together with the half-sister + some negative thoughts about ML because of his 'coldness'/lack of communication.
At the end of the day, they have both suffered through unfortunate circumstances and imo both the characters feelings/actions seem valid (as of current information provided to us), and it'll take time for mc to heal and properly talk it out with past ML (since it literally depends on mc because only she can go back to their timeline unless child Rutger somehow gains past Rutger's memories lmao)