How dare anyone tell you you are doing this wrong?
You are grieving. Whatever you are doing, however you are doing it, whatever you are feeling, and however you are dealing; that's your way of grieving.
Some people feel the need to weep and wail, others freeze, some get frantically busy, and others stop everything. Some people find they need to get everything sorted all at once, and some people need to shut everything away in a little box and take it out one tiny bit at a time. Some people need to fall apart, and other people need to stay together. And most of us do a mixture of any or all of the above. None of its wrong, it just is how it is.
You're getting on with life, well, life doesn't stop. So you kind of have to. That's not wrong. It's also not wrong to let some bits slide, to ask for help, to live on take out and sandwiches if you forget how to think about cooking for a while.
None of it is wrong. It is just how it is.
Two people will grieve very differently. Try to avoid the people who are telling you you're doing it wrong. They may mean well, but equally they may be grief vampires. I've had a few of them before. The latch on, and feed off your sadness, seem to need you to be visibly upset so they can comfort you, and get really affronted if you decline their offers or are actually functioning normally on the surface so they can't get in.
If you crave solitude, that's fine. If you want company, that's fine too - ask the friends who you know you can tell to bog off when you've had enough, and the ones who will laugh with you and acknowledge you are a complete person not just some grief shadow.
You do this by doing what you're doing, feeling what you're feeling. You put on a face for the children because children grieve differently to adults. Although it won't damage them permanently if they do see you upset too; it's ok to tell them you're sad/tired/flat/struggling because Grandma has died.
You loved her. Even though things weren't perfect, even through the difficult times, she was just there. And you had the option to visit, to phone. And now that's gone. And it is a physical pain. It does srown sometimes. You float on this raft keeping things together as you get the children to school, and then you loosen your hold a little and you're drowning. Deep waters.
It's ok. Even when it's very not ok. This is very early days. You do what you need to do in order to get through. And there will come a time when you're breathing again, when you don't need to try to work out how to, because it comes automatic again. And there will be other struggles.
But for now, break time down into however small a chunk you need it to be. Can't face a whole morning? That's ok. What do you need to do in the next hour? And if that's still to much, what needs to happen five minutes from now? If the answer is nothing, then just breathe. Cry if you need to. If it's get the children to school, then gather book bags and other bits, and head off.
Be kind to yourself. Eat something. Drink something. Breathe.