The house is a 1950's split level. I have a tub and shower that are back to back and when you run one, it backs-up in to the other. I have opened up the bathtub stopper and removed a lot of hair and grease using an auger. I have had a little trouble putting the bathtub stopper back in place where it flips up and down easily. (not sure if this is part of the problem) I ran the auger a couple more times and no more hair is coming up. I have no idea how the shower and bath are connected at the drain level. Any advice would be really appreciated.

The 3" toilet drain probably joins the 2" shower and both go into a 3 or 4" main drain. Your clog is after they all come together. You might have some luck rodding down the vent stack from the roof itf you can do that safely.