I think she is nuts.
If my mother died, I would request that my boyfriend be there with me the entire time.
I would not invite my ex to the wake
I would not point fingers and blame and start fights with my bf (unless maybe he was hitting on chicks at the funeral)
...but like you said.... maybe she is just different.
Regardless, playing mind games with ex's, etc, especially during emotionally unstable times such as a parents funeral. Not cool. I wouldn't even bother trying to maintain a relationship with someone like that.