I'm having to re-do a basement bathroom remodel due to a drain in the laundry room that repeatedly overflows due to the shower drain being connected to this drain it gets clogged with hair quite often. We have a drain cover which helps a little, however my question is, is there any way to do something permanently to the drain to prevent flooding and therefore cause mold in the bathroom to the point it ruins the floor boards and dry wall?

You can fill the trap with cement and seal the floor drain off. Regards, tom