Samantha, that sounds really awful. It hurts me to hear that your family isn't understanding. If you said, "I have high cholesterol - I can't eat bacon," I wonder if they'd be different. It's so cruel to not be accommodating, or at least understanding, about health issues. And even to assign you to cook a food you don't even like! That just makes me so angry.
In terms of the green been casserole and the sweet potato pie, I'm pretty sure you can make those safely. (Though since you don't *like* the casserole, I'm not sure you even care.) Here's a recipe for pumpkin pie that I bet can be adapted for sweet potato. At the very least, you can look at how this compares to a standard pumpkin pie recipe, and make the same substitutions for your pie.
I'm sure there's a way to make a safe green bean casserole - I'd do a google search for a vegan recipe, and then make sure it's not loaded with oil - but you could also be as considerate to your family's tastes as they're being to your health, and just make some other green vegetable dish that you actually *like*. You could also, though this is a bit of work, make alternate foods to what your family's serving - *safe* mashed potatoes, safe veggies, even some safe chicken. If they won't serve you food that's healthy for your body, bring your own.
The communication and consideration problems, though, worry me more. If you just want to deal with this one meal, then eat beforehand, or bring your own food, and tell them to go screw themselves. Obviously you need to protect your own wellness. That's more important than being submissive to their ridiculousness. But if there's any way at all, I'd suggest addressing the bigger problem - their resistance to listening to what you have to say and to respecting it. Have you ever sat one of them down, whent here are no distractions or teasing in the air and said, "I need you to listen to what I have to say, and respect what I'm doing for my health. If I eat this food, I will get sick." Any family who loves you should support what you're doing to make yourself well. This IBS diet is far from extreme or weird. If your family can't handle that, if they can't be serious and listen fairly for the one minute it takes to explain... Stand up for yourself, communicate clearly, and, above all else, treat yourself healthily.
ibs-a (mostly d) // vegetarian