In my day to day work, I have to assist people in facing this decision. And what I have found is that typically, no one really addresses it until they have to actually, for real, make the decision because insurance isn't paying for another hospital day and it is time to go. I think the parents are often afraid to bring it up and the (grownup) kids don't want to think about it - think about mom and dad being dependent, being dependent on THEM. We all tend to think "not MY mother/father".
The reality is, only you can make that decision for yourself, as the potential caregiver. Does she need someone 24hrs to keep her safe because she has dementia or falls a lot or is she physically dependent or bedridden from a stroke or other malady?
If you are home, have a reliable income that doesn't require you leave the house to work, and are emotionally and physically able to do so - your home might be the best place for her.
It can be very rewarding to care for your loved ones but it is also demanding, difficult work. And, it has been my observation that your siblings are likely to think you are doing it all wrong.
If you HAVE to work outside the home and do not have a strong support system, then you are kidding yourself if you think your parent will be safe because you cross your fingers every time you go to work for a few hours and leave the phone within reach. You can hire aides and sitters,adult daycare, but in the US, that is private pay (not insurance). Even home health is approximately an hour a few days a week, depending upon the services your parent qualifies for (IF she does).
Then there are those who could stay home and not experience an economic tailspin - they don't HAVE TO work, but do because it is a career, part of their identity. If this describes you, then you have to weigh your parent's need against your need to maintain this career, achieve your own goals.
If a nursing home is the most appropriate option, it doesn't mean you will never see her again. You have some options in selecting a home. If you wait until the last minute (ready to discharge from a hospital) and the parent has Medicare (including supplements and replacements), your parent is going to have to go to first available in the area, but you can place her on waiting lists in preferred facilities. You can visit often - daily, weekly, make drop in visits to check care across the different shifts. Have meals with your parent, get to know the staff and let them get to know you and your parent.
It's difficult to make these decisions. Even more difficult if the possibility of needing this level of care isn't discussed beforehand and if we don't even want to think about it at all.