You've gotten some sound advice so far
I think many of us have had this exact struggle at some point, when you're still living at home and you want to wear diapers and baby out, but you're afraid to because of x or y or getting caught... it's not a fun time, so your nerves are understandable, we've been there, hang in there
From personal experience, my Mother discovered my baby toys when I was still living at home and she freaked out, I can only imagine how she would have reacted had I had some diapers left in my stash
That being said, I didn't get rid of this side of myself, I just became more careful with how I went about procuring baby items, hiding them and finding the time to regress
It is possible to wear diapers and regress under someone else's roof, but you need to find a way to do so discretely. What I found worked out was timing things right. My Mother often left town for work related purposes, that was when I had the freedom to indulge. Maybe your Grandmother has something that can take her away from the house for a bit so you can regress... if she is a homebody though, that'll make things difficult
You could always try to wear covertly too, like wear a diaper under some heavy or baggy clothing. Maybe you could even try wearing thinner less bulky or noticeable diaps like store-bought brands or Goodnites... I know those aren't as nice as a true-blue (or in your case, pink) AB diaper, but sometimes to indulge, you gotta do what you gotta do
As far as disposal is concerned, you've had some sound advice; keep an air freshener on standby, double bag and dispose of them in the evenings.
Of course, one option that many ABs and DLs endorse is being honest with your family member. Telling or revealing this side of yourself to a family member can be hard though, not only is it too nerve-wracking for some, but in some cases, no matter how you spin it, they may not understand. The upside to revealing things, however, is that they might understand, if they do, that can make things less awkward and help with self-acceptance. Your Grandmother doesn't sound nosy or like the temperamental type, so have you thought of maybe confiding in her? That would make things less nerve-wracking and it would give you free rein a bit
At the very least, if you had a good hiding spot, I doubt your Grandmother would pry
In my humble opinion, the best thing to do is wait it out. I may have regressed and explored my AB side on and off when time allowed under my Mother's roof, but I didn't really have the freedom to explore things fully until I was out on my own. If you can grin and bear it for the time being, maybe waiting is the answer, after all, it is much easier to baby out when you have your own place
In the end the decision is yours and whatever decision you make I hope it works out. In the meantime, try to keep those nerves in check and do some soul-searching, I think you'll find the answer/solution that's right for you
