@Paul0101,
Your kids are grownups, yes?
So talk to them. Explain that this woman is very special to you, and that these are your last days and you would like to at least try for some happiness. Ask that they understand this and be at least civil to this woman; their politeness will go a long ways toward easing your mind. E. g. your kids don't have to like her or the situation, but it is your life and you are going to live it. You don't want to draw a line in the sand, you just want for there to be an easier time all around.
As for this woman, does she know what she's getting herself into? I mean really. If you are being given a hard date (pretty rare these days, is my understanding), then you would already be pretty damned sick. Be as up front with her as you can, so that she has all the facts. And explain that your kids are weirded out and that you hope they can be civil to her. Make it clear, too, that pain and debilitation can make anyone less than wonderful to be around.
And get yourself a second opinion. Seriously. Terminal diagnoses shouldn't be swallowed hook, line, and sinker. Perhaps there's something that can be done.
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