I'm so sorry OP. Would you like to tell us about him? Who he was? What made him special? I know it's cliche, but he will always be with you to some extent - he lives on in your children, and in you too, with the memories you hold of him, and the things you find yourself thinking and saying that you'll realise you 'caught' from him.
If you haven't already, let the children's school know so they can support them, and consider play therapy. There are books that can help children to process what's happened. Not just the obvious ones, like 'Badger's Parting Gifts', but more specialist ones that you can get through the library or online, that specifically deal with the sudden death of a younger parent. Have a read of them yourself before sharing so you can check they're appropriate. If you have a garden, how about making an area 'Daddy's patch' - plant a tree together there, and some flowers that were his favourite colour. You can lay pebbles the children have painted or hang homemade decorations off the branches of the tree, maybe have a low seat there that any of you can go and have a sit on when you specially want to think of/talk to him. When you feel ready to go through his clothes you can do it with the children and they can help you pick out his favourites, and the material can be made into patchwork teddy bears for the 3 of you, if you feel that might help.
As for the guilt you feel at not being able to save him, it's very natural, but the chances were very much stacked against him. My uncle was a hospital doctor and dropped down with a heart attack in A&E. Of course he had immediate professional assistance but he couldn't be revived. It's a tragic thing to have happened but please, don't blame yourself.