I don't want to invite my brother-in-law to our wedding
Why would you not invite your brother-in-law to the wedding?
I couldn't care less about him. I know for sure he will not show up.
It is expected to invite family members to your wedding. If they don't show up then that falls on them, but you should do the respectable thing.
He's going to be missing out.
He would be missing out if he didn't go, but you should still make sure to send him an invitation. You should invite your family members to your wedding to be more inclusive.