I honestly think your husband has a point that needs to be considered. As good intentioned as this discipline tactic may be, it does set up other siblings to see that the badly behaved kid gets to be with mom all the time and gets all of her intention. Thus, it isn't far-fetched that a child would conclude that the way to get equal attention from mom is to be just as badly behaved or worse in order to qualify for tethering privileges.
What may help alleviate some of that is if your son is required to sit in the same room with you while you are doing a positive activity with your daughter. Then he gets to see that while not being banished to his room is better, it still is a bummer not to get fun time with mom. It will also give your daughter a reminder that whether brother is attached to you or not, she still gets positive time with you without becoming a difficulty.
The only other thought I have is this - if your kids are not physically hurting each other or bullying each other, let them settle their own squabbles. I am reminded of when my youngest was in a car seat and would cry and blame it on his older brother who usually sat behind him in the van. Except one day he goofed and did it when his brother wasn't even in the van. I knew then I'd been duped into getting after the wrong kid because I couldn't see what was going on. After that the rule was, "No blood? No intervention.". Now that's an exaggeration, of course, but I worked really hard to let them settle their own arguments after that. And when they discovered that mom wouldn't jump into the middle of it, they quit fighting as much as a way to get attention from me.
Just a thought - take what makes sense and ignore the rest.