You sound like a driven and hardworking woman with a very clear sense of what you want to do with your life. And you're taking the right steps - plastering your dream companies - to get there. Because of that, I'm going to say that you're not wrong to disagree with your mom.
But, and there is a but here, there may come a time when you need to expand your search outside your ideal industry. If there are goals you have (live independently, buy a condo, lease a new car, start saving for retirement) and you've spent a year applying for every job in your dream career track you can think of with no luck, then there will need to be a change. Life is a balancing act for people on the outside of an industry they want to be in. Do they spend years trying to pursue it and sacrifice financial stability? Do they give up on their dream and focus on other life goals? Do they walk the line by getting a good job and not giving up hope for a great one? The answer to those questions are different for everyone.
I think your mom is trying to help you, but you need to let her know how important this career path is, and let her know how much work you've put in. And, for both her sake and yours, discuss a timeline with her. Perhaps you two can agree that if you can't find anything perfect in six months, you expand the net a bit. In exchange, your mom can be supportive and encouraging of the plan, so you don't need to feel so persecuted.
I wish you luck. Hopefully you get a call from HR soon.