How much do you want to explore?
Four days is definitely about the right amount of time. We typically recommend people drive no more than 500 miles per day in order to have time to explore a bit but still cover some miles. But that is our maximum miles per day recommendation. If you want a more leisurely drive with a bit more time for exploring, and also a drive that might better suit your mom's health condition, I would suggestion stretching it out to at least a fifth day. Of course, the more days the better if you want to have a leisurely drive.
I have a small 12-volt cooler (holds about 9 cans). I have mixed feelings on it. It can be handy but since I make a lot of stops, and since I worry that it will draw the battery down if left on when I'm not driving, I tend to put a ziploc baggie or small plastic container full of us in it to keep things cold anyway. I really don't think it's all that much better than just having a smaller cooler with plastic containers to put ice into (so you food stays dry). But, then again, I have friends who think it's the bomb. So, it can be handy but it's really not a necessity, imho.