The in-front-of-the-kids part is the piece worth addressing first and separately from everything else β not because the opinions themselves don't matter, but because undermining a parent in front of their own children has a cost regardless of who's actually right.
1. Address it in the moment, calmly and briefly: "Let's talk about this later, not in front of the kids." You're not conceding the point, just moving the venue.
2. Follow up privately, and lead with the specific behavior, not a character judgment: "When you correct me in front of the kids, it undermines me with them β can we talk through concerns privately instead?"
3. Expect some pushback the first few times. Boundaries that are new often get tested before they get respected β that's not a sign it isn't working, it's just the adjustment period.
4. Decide in advance what you'll do if it continues despite the conversation β shortening visits, or your partner addressing their own parent directly β and loop your partner in as a united front rather than carrying this solo.
This usually isn't really about parenting technique β it's about who gets to have authority in front of the kids. Once that's actually named, the specific disagreements tend to get a lot smaller.