Jessica - my views are this. When someone dies, the ONLY people with any degree of 'right' to be at the funeral are their immediate family - ie, their spouse, their children, their parents, their siblings. That's it. Not inlaws or exes or friends. Or people that an ex ran off with...Or their friends.....
Funerals are private for the family. NO ONE just 'turns up' uninvited. Not even to pay their respects.
If and as that sad day comes when you have to bury your husband, then if you don't want anyone there you don't want, that's it. To me, looking at your situation, the only people with any legitimate 'right' are you and your husband's children.
Funerals are not some kind of social event, or public demonstration, or come-one-come-all. They are the last goodbye for the very closest family only. If that is what the closest family want.
If necessary, why not ask your husband to write down his funeral wishes, and then you can show any 'uninvited' that you are carrying out his wishes, and that is that. You might also want to take the added precaution of having a friend or official 'on duty' at the chapel/church to prevent unwanted entry.
At my own husband's funeral, I didn't even invite my side of the family, not because there is any friction, but simply because my side is a very 'noisy' bunch, and they would have overwhelmed the occasion simply by their presence. I just wanted the time to be a quiet farewell from me, and my husband's surviving blood relatives who loved him so dearly.
As to your cousin's wife, I think she made the right decision in the circumstances, and no one should criticise her for it - they should respect her for it.