Raw meat in washing up water
You have a sensible approach, and for the right reasons. Food-borne illnesses don't die at the temperature your sink is at, to kill them you'd need water so hot you'd burn yourself, and even anti-bacterial soap would not be good enough to make the water safe. If you chlorinated the water it would be a different story but that's overkill when simply doing things in the right order will keep you healthy. 

I use the same approach as you most of the time, although sometimes I clean off my cutting boards first and then rinse out the sink before filling it. Either way I'm not letting raw meat float around in the same water I'm using to clean the dishes I eat off of. 

You're right and your wife is wrong - tell her that, she'll like that.