I'm not a fan of people driving drunk, either. But you admitted yourself that no refusal weekends and checkpoints are unconstitutional. I want drunk drivers off the street, too. But that's what we get warrants for. I don't think it follows to want a "fair justice system" and at the same time say that you're basically OK with violating the Constitution as long as it keeps drunks off the street.
Moral and constitutional are different things to me, too. But they can overlap. I can find something moral that is deemed unconstitutional. And I can find something immoral that is deemed constitutional. Just like I can look at something that is both moral and Constitutional.