Okay, my views.
The kids are old enough to be spending overnights with dad. If the only violence she can allude to is a stoush about car keys - that she obviously contributed to - then I can't see this being a reason for the Court to refuse overnight time. Reasons it might have for refusing overnight time is that overnight time has never been facilitated before, he took a long to apply to Court, which implies he was kind of agreeable to it, and the father's parenting skills haven't really been tested outside of the current arrangement, so the Court might take a gently-gently approach.
With that said, though, it really depends what mum provides as reasons against overnight time.
What's he actually seeking in interim orders? If it were me, I'd probably go for one overnight each week (Wednesdays), plus one overnight on his weekend, so three nights a fortnight right off the bat, but not consecutive so the kids aren't at risk of any real separation anxiety, then seek the extra two weekend nights incrementally - move to four nights after, say, two months, then the full five nights after another two months.
I don't think the Court will continue allowing mum to play supervisor when they're spending time with their dad, though. I read a case recently (though I can't for the life of me find it now) where the mother asserted that she was a suitable candidate to supervise the father's time with his kids, but the Court shot it down instantly, commenting that it would create a toxic environment, considering the conflict, and that the children would be very limited in their ability to build a meaningful relationship with their father while their mother was there occupying their attention.
