This is an interesting concept for a crossover, although the combined world is a bit confusing to me, like the way magic works in this world seems more complex than in the HP-verse.

I like the way you've laid out the family dynamic for the Crouches. They definitely seem like a realistic unhappy family, although it's nice that Barty at least somewhat gets along with his mother.

I was a bit disappointed that Light didn't show up in this first chapter, but I suppose we'll be seeing plenty of him later on...

[I'm you're wife] - "you're" is a contraction of "you are". The possessive pronoun is "your". Possessive pronouns never have apostrophes in them. Other than that, I didn't spot any typos or grammar issues.

Quite an interesting start, with a hell of a fight too. I actually thought it would end with Bartemius killing his own wife, and the Shinigami appearing right there, with Barty Jr somehow able to see them. Well, I have never read a story with Barty Jr as the main character, but this story took my interest. I am actually going to follow, in order to read what happens next. Note: Definitely want to see how are you going to portray Light in this story. I love Death Note! Hope you update soon.

This is a nice setup for a story that promises to be very interesting. I like how you modified the world to make this onw, and I'm curious about how will the crossover turn out.
I like Barty, so far, and how he sees both his father and mother. Poor Mrs. Crouch can say nothing to her son because he knows his father and how he acts. I love the idea of going to Japan in order to just get away from his family.