My understanding is that the decision to cut out House's leg muscles was made by his (then) wife, Stacy, who made appearances in Season 1. House, apparently would have preferred death and blamed his pain and disability on his wife and they divorced. Stacy has since remarried. Stacy and House had a brief affair (can't remember if it was Season 1 or 2) and, in the end, House decided that he couldn't wreck Stacy's new husband's chances of making the marriage work. Oh, and Stacy's current husband (Mark) also had some medical problem that I think resulted in his being confined to a wheelchair.
The tension between Dr. Cuddy and House is mix of sexual tension and a power struggle. In the most recent episodes, Dr. Cuddy is planning to get pregnant via in-vitro fertilization and House seems perturbed that he isn't being considered as a potential donor.