And you're absolutely right to do so. But you can never truly be sure that your work is the best it can be without reaching out to someone who isn't that close to you. It's good that your parents are more honest about what they're reading--that's a great start--but a truly impartial observer is going to be the best choice for a "beta reader," as they're called. Obviously, those are going to be hard to find at this stage, but maybe you could start reaching out to someone more outside your social circle. What about a trusted teacher or professor? As someone who has already had practice judging your work, they might be helpful.
Other than that, the best thing to remember is that you shouldn't necessarily be trying to send out a perfect novel the first time you approach a publisher. If you commit yourself to allowing only perfection, you'll never reach that goal, because improvements are always possible. Achieving competence and a high level of polish is important, but the other facet of that is knowing when you need to let go of a story and put it out there before you work it to death. Think about it--what does "the best they can be" really mean in this situation, other than frustrating yourself because you can't achieve perfection? The vast majority of novels published today have flaws, sometimes large ones. While you obviously shouldn't be aiming to write a flawed novel, there is always a danger of holding onto something you want to improve until it loses steam and grinds to a halt (there are a few good examples of this, if you want more detail, but I don't want to bore you...).
(As a side note, I do want to point out that my criticisms of the way reading is taught largely have little to do with teachers themselves, as most of them are just trying to do their best to adhere to standards. My above opinions have more to do with the standards themselves...)
You should give Austen and Dickens another try, especially now that you're trying to become a writer. But this time, approach them less with the idea of trying to get through the writing, and think about what's being shown. A lot of Austen's work is extremely satirical and hilarious, especially if you pay attention to the dramatic ways her characters act. And Dickens is a master of plot, so you can learn a lot from the way his stories are constructed. Reading old books as a writer is very different than reading them as a student, especially since you no longer have the pressure to read them quickly and absorb everything--you can take your time and notice more!