And how would changing dimension safe her?

If she changed dimensions, there would be two possible outcomes;
1. Kakashi wouldn't be affected, as his physical body would remain in the Kamui dimension.
2. She would take Kakashi with her to the other dimension, but Kakashi would blitz her as well, as he would charge towards her while being intangible (so Ice dimension to immobilize him is useless).
Fact is, she saw Kakashi charging towards her, yet couldn't do anything. She lost that clash. Even with no intel, she saw how the bone passed through Kakashi and saw Kakashi charging towards her, yet she simply couldn't react.
You can comport yourself as you want, insult, but all that doesn't change this fact. Kakashi isn't stronger than Kaguya, but the talk is about Sasuke. Sasuke can't do anything. If he teleports next to Kakashi and then strikes, he avoids it with intangibility like Kaguya by using her portal. You can like it or not. You can't compare Kakashi to Madara. Madara had no protection, he had just one Rinnegan with a Limbo that was immobilized by Naruto, Kamui is auto protection; Sasuke teleports next to Kakashi, strikes from close range and slips through Kakashi. That's how Sasuke's teleportation works. Teleporting next to the target and striking from close range.
Anything slips through Kakashi as he can just make himself intangible. Deal with it. You have no argumentation at all, you just be like "Thats insane, that's just a MS, how can you believe this?". It's all fact dude, deal with it.