In my experience it's definitely the work you put into it. I started my college journey in Beginning Algebra (Sad, right?) and moved onto Intermediate Algebra before even getting into College Algebra. I had Bs and Cs in all of those classes, not because they were too hard but because a) I wasn't trying hard and b) at the time I was still in self-doubt mode. I wasn't sure I wanted to put in the work required to major in a math/science field.
Once I was sure, my grades and study habits improved. I've now aced most of my trig tests, and once my final is over I'll be doing an independent 1 month study of precalc (just to brush up) before taking a summer Calc I course. I intend to ace that course. Getting a C in remedial math isn't as bad as you'd think, the math is easy enough that you'll pick it up again in the next course. If you've forgotten how to rationalize an equation you'll be doing more of it in College Algebra and Trig.
Like Micromass said math is cumulative, but as such you can review things as you go if you have the requisite drive to do so. It's just not a good habit to get into; at the moment it's easy and you don't have much to review. However as time goes on there will be more and more to remember (and forget) and it's good to catch your poor habits early, before they put you in a hole you can't dig yourself out of. As I hear it that point is Calculus, where mastery of algebraic manipulation is assumed. Hence my review of PreCalc.
Do the work and you can major in anything you want. If I'd listened to my family or my teachers, professors and advisors I'd be majoring in Philosophy. Not because it's easy, mind you, but because my intellect seems to be more inclined towards forming and refuting arguments -- but I want to do something else, something more difficult, precisely because it comes so easily to me.
As for lying, well, I don't see why you'd need to do that unless they're threatening to kick you out of the house if you don't major in their chosen field. Assuming this is not the case you could simply explain to them that you're more capable than they think you are, and you intend to prove it to them by majoring in YOUR chosen field. Communicate that you're leaving your options open, maybe compromise by taking an intro IT course (if your schedule permits), or at the very least explaining that many of the first courses in the CE/IT programs are similar and you can also switch to IT if your motivation wanes.