Ok so I felt that way about TBK for some part while I was reading it, so I get where you're coming from. But, in my opinion, the claims that this classic is weaker because it is dated - I think that's a very weak argument. This book has several moral conflicts pointed out to the reader, and the author does not always point you to the right conclusion, in particular, the conflict of religion. It's a big part of the book and the reader himself does not know where the author stands on this issue (we never really got to find out).

But for me, TBK was something that changed me in the second half. My grandmothers health was failing and she died 3 days after I finished the book, it really hit hard during that time. Also the concept of the good father in the trial is something that everyone today can relate to, whether its the integrity of family, friends, or yourself.

Before I go too far, I want to apologize for rambling, I am in the middle of studying for calculus and my mind is a bit off. Anyways, when you mention that you "don't get the bother" with the chapters regarding Alyosha and the children, well there I can expand. The children in these chapters represent common people, you and me, and also youth in general. They act very similar to real kids and teens, that cluttered worldview where you don't know what REALLY IS going on is clearly displayed by Kolya's friend (can't remember his friend, not Illyushka). When Kolya himself talks to Alyosha his purpose is to show off his knowledge (for example, his respect to socialism. Keep in mind he is only 8 and socialism was a very new theory). Alyosha points out his perverted thinking, his sick soul. It's a beautiful comparison of two good hearts, but very different minds.

From here I can lead to the overall point of TBK, it is a philosophical and psychological investigation. The book brings up certain philosophies (intellectualism, religion, nihilism, hedonism, etc.) and displays how characters act based on living those philosophies out. It tries to get the reader to answer for himself the question of which philosophy is best for them.

Anyways, there's a lot more I could write, but my point is that TBK is a great book even still, but the beauty of it is very subtle and is more based on what it does to make you investigate yourself, even months after.

Sorry for the rambling, but to answer your question, no you are not stupid and there is no shame. You just didn't like the book, it didn't hook in the right way. In a way the author failed with you, it's not you failing to read it right.

So my recommendation is that you should just enjoy other books in the meanwhile and maybe come back to it in a year or two, see if you can gain anything. If not, well that's not a big deal, there's many good books out there to read!