The gendered pronouns reveal something it seems the screenwriters were trying to keep secret.
Grace is initially quite closed lipped about why Dani is important in her timeline. She's adamant that Dani is important, but doesn't actually explain why. This serves to keep the information from both the characters and the viewers. It's a notable contrast to The ...
"Assuming that their time machines can displace them spatially and not just temporally"
There's nothing in the movie to suggest they have precise control over where they end up.
Grace appeared in the middle of a highway and the time machine ball burned a hole in the highway which she fell through. That implies (to me) that they missed their target by a ...
I can't find the exact quote, but the T-800 mentions that it can detect "temporal displacements" which let him calculate the exact time and location a Terminator would appear. Then Sarah interrupts him and says "That explains the 'how' but not the 'why'." That's pretty much all the movie does to explain it.
At some point in the movie, Grace says something along the lines of:
We are designed for short bursts of energy against the Terminators, not continuous effort.
Presumably the fights they get involved in exceed her time threshold. Note that multiple factors will not make it easier for her:
Grace just went through time travel. This process hurts, a lot.