Does my wife have a right to tell me to cut my mom out of our lives?

Moms are moms, what are you talking about? of course they intrude in raising their grand kids, and all the wife hating thing. the wife stole their son from them, as far as they think. that's why we have millions of mother in law jokes, because this is life. now, your wife has every right to ask for whatever she wants, and you have every right to ignore it.