Did you actually hear her make the call to police? DV is normally taken very seriously and officers come out pretty quickly, esp if a child is involved. When I called them on my neighbour's abusive ex, they came out in 15 mins. So why wait till after she's done a full day of work...? I'm amazed if she's this emotional, she was able to go into work rather than deal with this very serious situation first, that impacts her child and your family.
You really need to call the police, and talk to HR pronto - you aren't the right person to be managing her emotional state, her child's schooling, her work, and her potentially abusive ex on your own without professionals getting involved.
Also, what reasons has your DH actually given for not wanting her to stay? I imagine if you had a conversation, he would have elaborated.
My worry would be that the reason she's not calling the police or other services is - they've just had an argument, she wants space from him or to leave him stewing, and you're the easiest option to do it with (as you don't know them well enough to ask questions unlike friends/family). And will go back to him in a few days once things have calmed down. But knows if she just told you she wanted to leave her ex or they'd had an argument - you wouldn't be quite so sympathetic and take her in.
It's what my neighbour did with me.
Call the police - you'll know for certain then what's really going on.