I agree! She pursued a career even with the TM $. I believe she only became a stay at home parent afterward because she had Watson. And Cole is working even with the money coming in from the show.
When I said she isn't very independent, I meant emotionally independent. (However, I am sometimes neurotically independent and may be viewing from a skewed perspective.) Some people (like the other poster) might see the way Randy raised her as damaging because he allowed her to rely on him so heavily, but I think that all comes down to individual parenting style and the way you yourself were raised. I personally was raised more like Chelsea than anyone else on the show, and I am grateful for it.