Indeed, rabbits need hay for several reasons: it is neccessary for wearing down their teeth, it has all the right nutrients, and it improves gut function. Rabbits don’t get enough fiber without it, and that is very bad for their health. Why is your grandmother allergic to hay? Is she allergic to grass(pollen) or allergic to dust? Hay can be quite dusty too.
You’ll also find that most rabbits don’t like to sit on someones lap. Most of them prefer firm ground underneath them, so they can flee in case of danger. They also dislike being held. They’re prey animals and it can take a lot of time to get them to calm down enough to sit next to you for pettings. It took me half a year to get my dwarf rabbit to sit still on the couch next to me for a couple of minutes. He’s only cuddly on occasion, just like most rabbits he comes to you for cuddles, only at his convenience.
Take the time to consider if a rabbit is still the right pet for you. Rabbits are often portrayed as cuddly, but that’s exaggerated: they mostly prefer to do their own thing. This leads to many disappointed first-time owners. I hope you can find a pet that is just right for you and your family!