Is it possible to install a pump to fix a slow drain?
This almost sounds like a common problem with draining RV holding tanks.

You should try to support the drain hose from the tub so you have a gradual slope reaching from the tub/shower drain to the floor.  

I have a contraption called a "Slunky" which basically allows my RV holding tank drain hose to be very gradually sloped all along its run to a septic or sewer cleanout.