Well, everyone on here has given you condolences on your grandma. Grieving is a process as you are finding out that can take anywhere from one month to five years.
You have guilt that you did not or could not do more. You have your own family that comes first and then the extended family. Grandma knew this and did not ask you to move in with you. Your mom was single and living her life when the world turned upside down for her and she had to care for her mom your grandma.
Caregiving is a full time job even if it is for a short time. The caregiver has no one or if they do, it is a very very small circle of people to lean on. You give up yourself to care for another at all costs 24/7/365. Yes, you do get short tempered, you lose all patience, your ability to cope with any situation becomes short, and you may throw things like a child to relieve stress. When you can you find a way to stay away to find your inner self that has been lost to recharge your batteries so that you can carry on in silence.
So don't resent your mom for what she had to do with no break. Don't resent you for not doing more as you had your hands full with your own family. Let the ill feelings go. You cannot turn back the hand of time to make anything different.
Go to grief counseling if need be. Go out for a day in the park and sit and enjoy the fresh air, the birds and the breeze. Look at a flower and observe the beauty of it and if it is a rose, enjoy its fragrance. Accept that you cannot always change everything in life and let it be.
Now here is a big huge for you. Find a spot and grow a plant or tree in honor of grandma. As time goes on, the pain will go away and the memories will be great. She will always be with you and is watching you from afar. You might get a breeze or a bird fly by when there are none around and that will be her.
the other S.
PS I lost my parents at 9 and 14. Their memories are there but faint. I some times would like to have seen their faces with all the changes and technology that the 20th century created and have them compare it to their way of life. They were around with the Wright Brothers but barely so it would have been a good 100 year change.