Believe it or not, Max will be OK to eat later
...If this were me....I would try to stay in bed with them as long as possible and when I did get up, I'd start doing stuff around the house, of course, I myself would not eat anything. I would bring Madison to the Vet and when I got home, I'd feed Max...OR...You can feed Max in another room...OR...Leave food for Max when you leave to bring Madison
Best of Luck