I sense an aversion to consulting a vet... maybe you had a bad experience with a vet in the past but I assure you that the majority of veterinary professionals are not just looking to make a quick buck. As your friend told you, the diarrhea could be from any number of things and in order to avoid trying a bunch of unnecessary steps at home, you should find out what the underlying cause is so it can be promptly and properly treated. Don't assume that because she's an indoor cat that it won't be valuable to have a stool sample evaluated. I've been in the veterinary field for 10yrs and I've seen plenty of 'indoor only' cats with chronic diarrhea that were found to have a parasitic or bacterial infection. Considering her age, I would also be concerned about hyperthyroidism or a problem with her liver or kidneys.
YES, she should be isolated to minimize contamination of your home. As you described, you have young children that could possibly have accidental contact with the feces. Personally, I'm always baffled by how it is that pet owners 'deal with' things like this for such lengthy periods of time and then come to the conclusion that the pet should just be put down. It just doesn't seem like a fair choice. I strongly urge you to consider taking her to a vet before making any brash decisions. You've had her for 12 years... give her a chance!