I understand why you would like your children to see her one last time and they do need to understand the sad side of owning pets. I would just like to say that if she were to pass away at home, it can be very distressing and may look like she is having a seizure as she "runs to the bridge" and this may distress them even more. Maybe an option would be to let them say their goodbyes at home and then take her to the vets, as Sport Billy says it can be difficult over the weekend to get to the vets and this could result in her suffering.
One thing you could mention to them though to comfort them is the story of the rainbow bridge and how she will be living over the bridge, no longer ill and back to how she was when she was young and healthy.