People hosting parties often share their menus. It’s not really for approval, but more of a courtesy. For someone with a dietary restriction, if they don’t see something they can or want to eat, it’s an fyi to bring something that works for them.
She does not like dippy things? Something tells me she is not going to be a vegan soon… 
“Something I was thinking about which nobody pointed out, is that clearly the cousin was offended by the initial response because she shared the text (and her sense of offense) with the sister. That’s what prompted the sis to reach out to OP, probably in hopes of smoothing things over.”
This is pure conjecture based on what has been posted here. It might be true but not enough details here to assume it. Perhaps OP or her husband shared the info with his sister, not the cousin.
“Perhaps OP or her husband shared the info with his sister, not the cousin.”
Correct!
I don’t think the text by H was rude at all. And it’s fine that she told beforehand that she’s vegan so nobody is asking why she’s not eating or brought special food to the event…
SO simple for cousin to bring something for herself in case nothing else happened to be available for her. She’s got as much time to put food together (especially for herself alone) as anyone else does. Expecting people to cater specifically to your needs while hosting a big party is very rude in my opinion.
I think there is a lot of different things going on. I don’t have a problem with the cousin letting you know she is vegan. As a host I would want to know. In my opinion your H text was flippant but my H would have done the same. The cousins text messages with the sister adds light to the matter that the cousin is inmature and spoiled.
The comment that you won’t have time to get something to a accommodate her I think is an excuse. Break the fast is over a week away. Food can be purchased several days ahead and I highly doubt you won’t be at a market before that time. It’s fairly easy to pick something up from the deli counter. Or just buy her a sweet potato and stick it in the microwave. Though this cousin sounds like the type of guest you make an effort to accommodate and she decides she is eating meat the following week.
My D has a whole list of food allergies. She knows what she can and can’t eat. She doesn’t expect anyone aside from her mother to accommodate her. Yet it is really nice that the person we are going to celebrate with has asked what foods to avoid.
@mom60
Just curious…what’s at the deli counter that is vegan? Remember…that’s no meat, fish or poultry, no eggs, no cheese, no milk products.
And this cousin is picky about her vegan foods to boot.
OP - Do you have a Whole Foods near you? Lots of vegan items there. Heck even Walmart has vegan items or you can order food if you’re comfortable, from Amazon
I wouldn’t order a single thing. This young lady has already poo poo’d a a suggestion by another relative…AND the suggestion that she make the meatless chili and bring it.
There is no guarantee that anything is added to the food table will be to her liking anyway. She sounds picky…in addition to being a vegan.
@thumper1 - my market has many items at the deli counter that aren’t "meats and cheese ". They have signs that let you know if something is vegan, gluten free, dairy free, vegetarian and even nut free. They have roasted mixed vegetables, grilled vegetables, grain salads with no cheese and a vinaigrette dressing.
Being vegan isn’t a rarity these days and grocers do cater to them as well.
Please just make or order a green salad and be done with it. Many will eat it- not just perhaps ms. finicky.
OP if you have to go to the grocer between now and the dinner to pick up ice or beverages you can pick up a can of Amy’s Chili. When the cousin arrives give her a microwave safe bowl and let her fend for herself.
It’s not what I would do, but it seems like a safe middle ground.
Once again saying that peanut butter has no place in large gatherings.
Better yet, open the can ahead of time and put the contents in a bowl and tell her you went to lengths to make it especially for her. 
Cousin might not eat the bread if it’s challah due to the eggs. And I’ll bet she doesn’t like the seeds in rye bread.
And she might. It like canned chili.
I like the plain salad idea. The other guests will like that too.
But you already have veggies. Any fruit? If so…just let this go!
So, @maya54, as I wait for DH to get his herring and tomato ready for our little break fast, inquiring minds gotta know: what did the cousin eat?!
While it can be difficult to accommodate an "exotic " diet, I would rather do so (easily and simply) than have a guest who has nothing to eat. @doschicos advice is gracious and excellent. If you can accommodate less well, tell the guest what you WILL have aND tell them you won’t be insulted if they want to bring something to supplement that.