There are three parties in a marriage: husband, wife, and God. “Child” is not one of the parties in a marriage. If your parents are having marital problems, that’s on them. It’s not your job to mediate between the two of them, nor, frankly, is it even appropriate for you to mediate between the two of them.
Look at it this way. They’ve clearly been together for over 20 years, because they raised you and your brother. They did that without either of you being in a position to help them. Unless someone has suddenly developed dementia (which I doubt, based on what you describe), they should be able to manage without your help.
On top of that, if they expect that you’re going to be around for the rest of their lives to live in their home and look after them, what are you supposed to do after they pass away? Not to mention, getting a Ph.D. takes time and money, and that’s time and money that you won’t be able to offer them as you’ll be very busy. How do they expect you to support them while you’re going to school?
I would definitely recommend counselling. Your pastor would be a good place to start. When you present your plan to them, I’d make it very clear that this IS what WILL be happening, and not that you’re trying to get their advice. If they start to pull the “you’re abandoning us” card, just state calmly that this isn’t what you’re doing at all. If they get very emotional, you can just say, “Mom, Dad, I can see that you’re not in a fit state for us to discuss this right now. I’m leaving the room and ending this discussion until you’ve calmed down.” (That’s not disrespectful. It’s a statement of fact. If they want to behave as if they’re spoiled children, you frankly may need to treat them just as you would a spoiled child. The risk is that if they learn that guilt-tripping you and having a fit works by playing on your sympathy, then they will guilt-trip you and have a fit EVERY TIME they want something from you.)