If he is "ignoring you", then there literally is nothing you need to do. He lives in another state. Unless you feel like he is deliberately avoiding your brother because of you, then leave things alone, and just be nice when he's around, but don't "do" anything about this. You can say to your brother "I hope your brother isn't avoiding us because of me or anything" or you could send a note to the brother saying, "This may go without saying, but I hope there is no weirdness between us and I'll always be happy to see you.." or whatever.
But it sounds like you may be over-thinking this. What do you mean he's hell bent on ignoring you? Do you keep trying to get him to acknowledge you? If not, then he may just be busy. Guys are MUCH different than women.
He may not be over you breaking up with him, OR he may just not like you that much as "that chick from the past who broke up with him" OR he may not care at ALL anymore, so he's not reaching out, just like he wouldn't to ANYONE married to his brother, if he's not the super friendly type.
For what it's worth, I have no contact at all with any spouses of my siblings other than if I see them face-to-face randomly at family gatherings. Which isn't often at all since they live out of state. I don't FB them or email them or anything. Why would I?
There is no one way to handle this. Ideally, you all get along fine. If he's awkward with you, and never comes around, you shouldn't really "do" anything about it unless your husband asks for your help.
***K, um, my answer is too long now that you cropped most of your question out :-0!