Husband must cleave to his wife, they are now their own family, and the husband needs to set up firm boundaries with both his parents and the in-laws. In this case it seems the groom's parents are not the problem, but rather the bride's. Sometimes I've found it useful to have the wife address issues with her parents first. Then if the hint isn't taken I typically come in later and make things crystal clear.
My wife and I have issues with her parents flying cover for our children to avoid spankings (I.E the grandparents not telling us who hit who), as well as her parents arguing with us over spankings when we're in the middle of trying to discipline the kids (telling us that one of the children doesn't need a spanking and telling us that they're sick and tired of spankings, etc). We both agree this is unacceptable.
We handled it by the wife flat out telling them we are not interested in their opinion on this matter. And then when they refused to listen I later made it clear that we don't want them to leave, but if they insist on interfering with us raising our children according to God's Word they will not be welcome. That has stopped them for now.
Something similar needs to be done in this case.