May I ask why your parents are so against a gap year? Few years ago, I was in the same boat--feeling not 100% ready to apply to school, but pressured and ultimately forced by my parents to give it a shot. I was ill prepared and honestly wasted a lot of time and money in that initial application. Having gone through multiple cycles, and done the "gap year", the "I'll apply immediately after the cycle", and finally the "take a few years off then apply" I can tell you that the gap year(s) for me were super helpful, and something I truly needed to get me where I am today.
For me, my gap year wasn't used to tangibly raise my stats or anything--I took a few classes here or there, but my GPA was basically static. I also re-took the MCAT, but that's more because my score had expired from the first time I took it 😛 For me, the gap year was a chance for me to take a step away from the craziness that is being a college pre-med, get into the "real" world, and a time where all of a sudden, I had to make conscious decisions and choices to pursue activities and opportunities that helped me pursue med school. Trying to work fulltime, support yourself, AND adding on things like volunteering, classes, shadowing, research--it's HARD. It will test you and I think through this, if you can come out on top, your application will be stronger, but tangibly in your list of accomplishments, but also intangibly in developing your character and perspective on the journey you're going to take to become a doctor. And heck, post-college life working fulltime is great. You can have some disposable income, make some money, and attempt to to save up for applications/school!