Any plot involving time travel is going to be dumb, because time travel itself is inherently dumb. There's no real avoiding it. You compared it to Terminator when we first spoke of it, and it really is just Terminator, but without a Mcguffin child. An AI construct goes back in time to stop a human vs AI war in the future, but thank God this time she's not screaming about JOHN CONNER. Terminator never took timeline fuckery into account either, and it was still fun so I can suspend that plot failing pretty easy.
Episode two did end in a really awkward way, but I believe that INSTANT transition was necessary because them "shaking on it" was literally the last scene, and the next opens with him lamenting that they- well, just shook on it -so going from that to "no wait, I changed my mind, must save loli friend you accidentally revealed to me is going to die in the same newspaper that covered the bombing" was definitely rushed, but still established enough of what it needed to. Vivy, for as simple an AI as she is, still has emotions she probably doesn't understand, and acts upon irrationally.
The lead up to this actually partly covers your complaint with the butterfly effect, or timeline alteration. Matsumoto says that some
alterations to the timeline are acceptable, within reason, but it's otherwise forbidden.
Episode three opens with this concept again, where Matsumoto tells her she mustn't make unnecessary "calculations" based on the fact that Estella is her sister. She must be eliminated regardless. But Vivy's heart is going to get in the way of that.
General look and feel of the show you don't like... Well, there's a lot like pic related, and Vivy's demeanor and character that basically scream Violet Evergarden
which just makes me like it ''more';. But with a little bit of Terminator, and each phase of this 100 year plan seems to be laid out like Hitman missions, which I think is funny.
A seemingly emotionless Vivy, in disguise, is hyper efficient assassin/infiltrator/body guard. Hopefully the next ten episodes remain just as fun.