How do we convince our parents that they need to move so we can care for them?

My parents refuse to move and insist that my sister and I move in alternately to take care of them. Both of them have health problems that are getting progressively more serious. My sister and I both live several states away and are married. Our parents think we can leave our husbands for three months at a time to care for them. They become angry when we suggest that they move close to one of us and insist that the only answer is one of us being with them. My sister is saying she will go live with them, leaving her husband behind. I feel we should be united and refuse to leave our families and homes. Help!