I don't think there's anything else you can say that will change their minds. I am going through that route, though.
I went for LPN and opted for the two-year program over the one-year program. The second year I decided to apply for the LPN-RN at my CC. This was around February 2017. I was in the middle of my OB rotation. Every weekend I was sick. I was also working per diem nights at a group home. I needed to retake the TEAS test as the program wanted a more recent score. So I took it in February. I got an 80-something. I graduated from my program April 2017.
I took an online class that was needed for the program from May-August. I took the NCLEX in July 2017. And as soon as I got my "unofficial" result, I began applying to as many places I could daily. Many asked for a license number, so I'd just save those applications and return once I got my number. I had a few interviews. Most of the offers were per diem or part time, but I accepted a full time position at a dialysis clinic in August 2017. The pay is significantly less, but I needed the benefits. Plus, I only work 3 days a week. I started working in September 2017. By around November I found out that I was accepted into the LPN-RN program, and I started January.
Because I took the majority of the GE classes, I only need to take nursing classes and one GE class to get my degree. I'm also working and gaining some experience. Sure I want to pull my hair out most of the time, but I have loans from my first bachelor's. And seeing that number decrease each paycheck has been super satisfying.
So I'll just make up a hypothetical situation if I were in your shoes and applying to my CC's LPN-RN program. Say I did a one-year LVN program that starts in September 2018, let's assume that I take the NCLEX a month after graduating, which would be October 2019. Unfortunately with the CC, they only admit students once a year and the deadline is August, so I would have to wait until the summer. But I'd still be able to get a job, gain some experience, etc until then. I then apply by the August 2020 deadline. I start the program January 2021 and finish with my RN May 2022.
Yeah, that's definitely more work than just going directly into a 2-year RN program. A nice benefit to being an LPN first is that you potentially start working sooner (in this case 2019 instead of 2020). So there's that potential to learn and hone new skills, see if you really enjoy nursing, make connections and build a rapport with your coworkers. Many places also offer tuition assistance, so perhaps that might be something you're interested in? Just be sure to read the fine print as you may have to sign a contract that requires you to work full-time for 2 years or so after completion of the program.
Once again, I'm not sure how you can change your parents' minds. I know when I was initially going for LPN, my parents kept asking me why I didn't go for BSN or the accelerated BSN programs. They also never accepted my answer, but once I got my license, and moved on to the LPN-RN program, they stopped dwelling on what I could have done or "should have done." And if you do decide to pursue this route, I hope your parents also become more supportive.