This happened to me a couple of months ago. Out of the blue.
Yes, there was someone else involved but ultimately husband was literally just going along with events and not involved with feelings for her. He'd lost feelings/emotions full stop, if that makes sense. Started a sequence of events that he was being pushed along with (by other person). And felt that he couldn't stop them because he had nowhere else to now go.
Ultimately, it has boiled down to him not handling our younger child's disabilities (something he had always said he couldn't cope with, even before DS2 was born). And consequently, despite us looking like a strong couple, coping under difficult conditions, what was actually happening was that we were "polarised" and I was immersed with home/children, with no input from husband, and he was immersed in his working life (and diy at the weekends!).
It actually took him over 3 years after the diagnosis to reach his "crisis" point, where he was ready to face up to things, by which time he'd been uninvolved for so long, it was extremely hard - he felt impossible - to become involved.
And by this time we were dealing with our separate "responsibilities" - I thought working long-term as a team, he thought alone.
Add stress into the equation for good measure. He hit a crisis point.
Was adamant that he had fallen out of love with me. After 5/6 weeks, he suddenly clicked just what he wanted, and how totally disgusted he was by his (totally uncharacteristic) behaviour.
He's now going about changing things at home, spending time with DC's, helping more, and being totally supportive of me. It's like a huge wake-up call but one that, I think will help us.
He's also having counselling.
Sorry to waffle, but I just wanted to post because, like your dh's sister, I didn't know anyone else was involved at first, and was in a spin trying to make sense/improve things.
Even if someone else is involved, it doesn't necessarily mean worst possible outcome. Think I just want to let you know that he could have hit some kind of crisis in his head, and actually be in a place right now that he doesn't want to be.
Agree that your best course of action is to be there (phone/visits etc) and ready to listen and help with any practicalities. She will be speculating (probably wildly). Don't join in!
I hope that it all works out for them, whatever the cause and outcome is.