"With the exception of" means not including. "All of the students will go on the field trip, with the exception of those who haven't gotten their parents' permission." "With the exception of monkey, dog, and peeps, I'll eat anything." "the sense that" could mean different things. "IN the sense that" can help make something clear or explain something in more detail. Or it can mean "in this way / meaning". "She's not very friendly when you meet her. I mean in the sense that she isn't usually the first person to greet others. And she doesn't talk a lot. But really she's a nice person." "He doesn't use the word 'religion' in the sense that most other people do."

with the exception of X = except X = other than X = besides X I think you must be seeing: "in the sense that" It means something like "In the way that", or "in this way", or "for these reasons", or "because". I think school is better than work, in the sense that you learn a lot more. Is education the most important thing for a child? Yes, in the sense that education is necessary for success, no matter what the child will do when he grows up.