I strongly urge closing down the option of ‘staying long-term’. This will not solve the problem or make your grandchild’s life sustainably safer or better.
Engaging with the local WA & DV support is essential because there are well established protocols, guidelines & legal obligations on the support agencies & local services to support the abused, abuser (indeed so) & vulnerable children. Dodging or ducking police attention if required is a grave mistake.
To be completely blunt & forthright @LibbyR, as much as you are kind, fair, reasonable & well-meaning, you are the alleged abuser’s mother which muddies the waters in many ways. The young mother’s background that you have described suggests that she is vulnerable - dare I generalise widely to say, possibly very insecure & unconsciously manipulative- & by no means excusing your son’s actions or blaming the victim, this is their relationship & not your responsibility. The coming days could see them reconcile & then your kindness will belong to a period of time they may choose to overlook, for you to be yourself pushed away & kept from your grandchild. Do I speak from experience? ‘fraid so.
Oh, & I have to ask, what is your son’s account?
Has he incurred abuse or injuries?
You need to keep yourself well, boundaries strong, & neutral in approach.
Getting WA & DV support agencies engaged is urgent & important.