what an absolute nightmare situation, so sorry you are having to deal with this.
Firstly you have not wrecked any lives, you H did that when he started having an affair again, after you had forgiven him, you are absolutely right to end it, and had you just happened to find the information without your H being ill I guess you would have ended your marriage, no third chances, him being ill does not change that, just delays it.
Of course he is going to say he is sorry and he loves you, he is vulnerable, scared and facing his own mortality, would he have said that if he wasn't ill, I doubt it, he would most likely have left you high and dry whilst galloping off into the distance with the OW.
At the moment you need to think of yourself and your kids, they will be devastated, and scared, imagining the worst. They are old enough to understand that their dad is ill, and at the moment they cant see him, tell them that is what the hospital said, and that as soon as possible they will see him, reassure them as much as you can that he is ok but not well enough to see them. If you are sure your marriage is over, I would maybe say to them what someone else suggested about Daddy being in love with someone else so you will not be together anymore, that could be to much for them at the moment though.
you dont have to visit if you dont want to, you owe him nothing, he deserves nothing from you, do not allow him to use his illness as an ace card to manipulate you, do what is best for you emotionally, physically and financially. As others have said start to prepare for your future without him, get paperwork organised, arrange a solicitor, speak to the hospital about ongoing care, if you feel up to it, maybe send a message to his family briefly outlining what he has done, say you hope they will support your children at this difficult time, make it clear that you will not be responsible for his ongoing care when he leaves hospital, fuck what they think. Speak to RL friends and your family so they can support you.
finally lots of luck to you and your children, it all horrible, complicated and raw at the moment, things will approve