Under what circumstances can other family members acquire legal control for elderly relatives?

My 85-year-old grandmother had surgery a few months ago, and despite being told that she should do well, she ended up with a ventilator. She's essentially an invalid now, and we're told that she will dependent upon the ventilator for the rest of her like and that she requires round-the-clock care. She's unable to care for herself at all...she can't even get out of bed or hold a magazine to read. However, my grandfather is saying that he cannot afford to hire anyone for in-home care nor can he afford to put her in a ventilator care facility. He says he will take her home and care for her himself. He's entirely in denial about his own abilities and what is required to take care of an invalid. He's 85 years old and has fallen on many occasions. When my grandmother was able to help him, it could sometimes take him hours to get off the floor. He can't remember to take his own pills, much monitor my grandmother's medical needs. Despite the training the hospital provides, there's no way he will be able to do this well or properly...he would have to suction her lungs, take her speaking valve in and out, make sure the flow of air is consistent, monitor her oxygen & CO2 levels, make sure she's getting consistent feedings through her tube...and keep all the equipment working properly and cleaned. Having seen his bathroom, I know for a fact that's impossible. Not to mention that he's 86 years old. If something happened to him while he was caring for her, they would both be alone (no, he won't consider a First Alert), the consequences would be dire. My grandmother is still in the hospital for at least another couple of weeks. Is there anything their children can do to gain legal control over this situation?