IC, I'm going to give you similar advice to what I said to your W: don't overthink this too much. Your feelings right now are in turmoil. There's no right way or wrong way to feel. Feelings come and go, like storms over the ocean. Lots of things influence them. I'm sure you've had the experience of feeling great one minute, and then something happens and you feel like cr@p-- or the reverse... you feel awful and something happens to change your mood suddenly.
Don't put too much stock in your feelings. They are guides, but they are not a good source of rock-solid, long-term data about who you are at this moment. And right now, you're on a roller coaster ride.
For us eavesdroppers on your life, it started on this BB with all the convo about your dad... then you revealed the cancer... you and Miss IC have been close, scared, apart, clinging to each other, running from each other... don't try to make SENSE (in the sense of "logical" sense) out of all that. Don't discount the event with your nephew-- a very emotional event where YOU stepped into the role of your DAD... I feel the spirit of your Dad was very near during that. And no you weren't any way too hard on him.
[You know hunting is a sensitive area for me, and hunters must behave responsibly. My late H and I owned some property pretty far from where we lived and one of the neighbors there called us and told us that some people had gone over our fence and hunted. They killed everything in sight-- ~20 animals-- and just left them... fawns even, and the young bucks (I forgot what you call them)... in a big pile. Clearly they were just killing to be killing... every time I think about it, I want to cry and throw up-- such disrespect for life is disgusting... Maybe those people wouldn't have done that if they had learned respect for the animal from their fathers or uncles. Or maybe they were just scum.]
Think of yourself as being in a small sailboat on the ocean. The waves come, the storms come, the sun comes out, it goes away, it's calm, it's turbulent... but through all of it you're in this boat that has this thing... I don't know what you call it, because I'm not a sailor (although I did enjoy all the Horatio Hornblower books AND the TV series), but it's pointy thing that sticks out of the bottom of the sailboat to help keep it upright. Well, while the wind and rain are blowing your little boat around (those would be your feelings), the pointy thing under your boat goes all the way down to the bottom of the ocean, so there's NO way you can drown and be lost.
Some days you seem to be steering the boat, some days the wind pushes you, some days the boat is still, and some days you're lying passed out on the deck. The boat is safe AND ON COURSE at all times, whether or not you're consciously steering it, kwim?
Don't look to your FEELINGS right this minute (and the same goes for you Miss IC) for accurate data about your life and your relationship.
The feeling that the only reason you're fighting this is because of your W and kids-- nothing wrong with that. The fact that Miss IC admires you for traits you don't feel you possess-- nothing wrong with that either.
The chemo and other recent events are wreaking havoc with your thoughts and your emotions. And the enforced inactivity is giving you WAY too much time to think. When my late H was waiting for a kidney transplant (and it was also in the fall, during hunting season), he got a huge complicated model airplane kit and kept himself busy with it. He'd never built one before. I still have it hanging in the house.
I read a great quote from St. Francis of Assisi yesterday (patron saint of animals)-- and this is good advice for you and Miss IC these days: "Preach the gospel at all times. When necessary, use words." Obviously, you're not "preaching the gospel," but it's possible to talk and think too much. You can get caught up in the maelstrom inside your mind. Try not to give in to it too much. Many people have gotten through cancer and chemo and you can, too.
If you don't want to talk about being vulnerable, then don't talk. Just hold hands. You and Miss IC can establish a practice of connecting physically (kiss, holding hands, long hug) and skip the long analytical talks for now.
There's nothing wrong with the way you're feeling. Even when your feelings are uncomfortable, they're not wrong. If you want to label yourself a liar, I guess you certainly can... but who of us can accurately characterize him or herself with a label that holds true at all times. Labels are really pretty useless. You don't have to hash everything out and analyze right now. Just reach out for comfort while the storm rages. The sun will come out eventually.