I really do feel your pain and frustration. You are going to have to do something that is painful. It will be painful eaither way. There is not an easy solution here and that is what is making it so difficult. You can not avoid pain in this situation. What you can do is decide to takle action and live by your convictions. Remember this: A happy marrige is the best gift you can give your child. But a terrible marriage based on guilt or obligation will bring out the worst in the both of you and that will be passed on the your innocent child. The child will be impacted by the negatives and it will be then a part of him the rest of his life. It will impact how they form relationships and the expectations they have for themselves and others.
I'm not saying to immediately divorce her. What I'm saying is you can not put up with the solution she has chosen for you. I suggest you lay down firm boundries of what is acceptable behavior in your marriage. Then stand by them. Get into MC ASAP. If you really can't change the relationship then get out. You can be a great father with out her.
I know the medical issues are tough but the marriage and the child are her responsibility as well. When you decided to marry someone and have a child it is a huge responsibility. You both must discharge your responsibilities. But that doesn't mean you must give up your life and happiness so she can have a free pass.
Good luck my friend,
Vorlon
This advice may well end your marriage. It's better to work through the steps to improve the relationship are are in.