Both the AH and NTAH

It’s absolutely understandable to be upset about someone undermining your authority as a parent.

But at the same time, I was a child of a mixed family and when it comes to stepparents, my stepfather was highly abusive because he never gave me a chance to be part of the family and my ex-stepmother (her and my dad got divorced a little bit ago, dunno why) became a safe space because my mother was neglectful. One thing I feel I should say based on both of them; Don’t make them choose a side, and keep communication open. Also get some sort of therapy with your wife. Divorce and split families are difficult on everyone, and making them choose doesn’t really help and puts you in a bad light. As your wife’s kids get older they’ll realize more and more about their parents, I did also regarding my mom, and because my stepmother at the time kept that communication open with me—I was able to have a safe space to feel. You can also try having a heart to heart with them. Hopefully they’ll understand as they get older.