My dm is in hospital after falling at home.She is not Ill but will not discharge her until a care plan is in place ,she will need carers going in. If your parents have carers how long roughly did it take for it all to be put in place?
If it is carers at home it can be organised in a couple of days. Whatever you do, don't let them discharge her on Christmas eve or the day before as there won't be any backup or to call if no one turns up (as often happens)
It completely depends on where you live. I've worked in areas where a care package can start the next day and others where it takes 6 weeks! The nursing staff and occupational therapist should be able to give you an "average" time based on other patients but it'll depend on what your DM needs - larger package will take longer.
Wishing her a safe and speedy recovery. Yes, avoid end of week/bank holiday discharge if possible.