I am so sorry you are going through this. Like many other responses, this is a deal breaker for me, but it may not be for you. I second the idea of talking as openly as possible and trying to find out what is really going on....Sounds like something else is happening and the dog issue is just a symptom.
As to shedding, you can improve it by using different tools and to a degree by making sure you have a good diet to promote healthy hair growth. If you have a shop vac with a reversable flow setting, you can blow out the dog (or take him to a groomer for the first time to see how it can be done with a kennel dryer). The amount of hair your can remove is amazing.
Investigate thinning rakes such as the furminator, mars coat king, mat buster. They remove considerable hair (do be careful the tines/blades) be careful as the blades/times can also damage skin. Weekly brushing with one of those tools, a good pin brush and finish with a boar hair brush and the amount in the house will go way down.
Get a large spray bottle or one of those pressurized hand held sprayers from the garden department of a local hardware/wally world. Use that to moisten the coat prior to brushing. Also do a very LIGHT misting before swiffering, hair will be collected far more effieciently.
Good luck and prayers for a good outcome.