petite's suggestions are interesting and worth a try, although I'm surprised that something as acidic as grapefruit juice would be good for a sensitive stomach, especially when combined with vodka!
I have a friend who recommends taking a potassium supplement after drinking to prevent hangovers, although I think it depends on how drunk you are in the first place. I have tried it, along with plenty of water and an ibuprofen, and the combination seems to help. I'll also try to eat a little something before going to bed, like a banana, toast, crackers, a bowl of cereal, or an English muffin.
It's counterintuitive, but the stomach is supposed to be acidic. A big mistake a lot of people make is trying to raise the pH of their stomach with antacids, which causes an overproduction of acid in the long run. It's a positive feedback loop that increases one's stomach acidity over time.
I have never heard of potassium affecting a hangover before. Alright, I just looked it up and it suggests that replenishing electrolytes will help a hangover. That's the only thing I could think of also. Yes, Gatorade will help, but not as much as NAC or glutathione.
Trust me on the NAC or glutatione. The NAC or glutathione will prevent hangovers. I'm too lazy to explain the metabolic pathway of alcohol metabolism and how it produces acetaldehyde and how NAC or glutathione prevent acetaldehyde toxicity and how acetaldehyde is the toxin responsible for giving you a headache and causes cirrhosis of the liver and brain damage. Just trust me. NAC is what they'll give you in an IV if you drink too much and end up in the ER, because it will save your life. It saves your life the same way it will prevent the hangovers.
I actually recommend glutatione over NAC, though because too much NAC gives you stinky farts and glutatione will not. Your body metabolizes both quickly, so you can't take a large dose all at once and have it be effective, which is why I suggest once before you begin drinking, once before bed, and maybe once the next morning. Too much all at once and you'll just have gas. If you feel like you need more, spread your doses out. Take it once an hour, or once every two hours.
Too much of either one will deplete certain minerals which act as co-factors, such as copper and selenium. If you plan on drinking very frequently or taking NAC or glutathione frequently, you may want to add a mineral supplement.
I would also add that you should resist adding sugars or sweet liqueurs to the grapefruit juice and vodka, because that will irritate your stomach. I personally like the taste of grapefruit juice and vodka.