Bathroom drainage: bath's water flooding shower
Assuming this is a newly manifested problem in and otherwise regularly functional drain system, there are 2 things to do first: 


Insert your snake into the plumbing system through the shower drain, not the tub (you will have less chance of coiling it up on itself) and measure how far it goes before it hits the hard stop.  In case you don't understand, you want to have the snake be rotating the whole time you move it through the pipe.  It's designed to auger its way along and create a spiral cutting action inside the pipe (If this is a manual snake, go and get a powered one or one that has a small shaft on it to be turned by a cordless drill). My first suspicion is that the hard stop you are feeling is the elbow on the outside wall where the bathroom drain plumbing exits the brick.  If the auger stops at that distance, you can just keep pushing while rotating to get it around the elbow.  Then you can see if you can clear anymore out of the pipe.
Since the above almost never works to get rid of a blockage like what you are describing, the next thing to do is remove the inspection cap.  It's probably just cemented into place.  Just cut it off in such a way that there is a small piece of pipe left for you to cement a new cap in when you are done.  This time, install one with a removable clean out plug or cap.  Once the cap is out, run your snake through the pipe as far as it will go and see if you can cut the clog out with the snake.  Don't be afraid to run it for 10 or 15 minutes to grind away at the inside of the drain and remove all accretions.


It's hard to tell from the photos, but I don't think you have enough slope on any of your drain lines - they almost look level - and this can lead to accretions in various areas.  That might explain why you are having issues.  It may have been installed by a dummy.  That could help to figure out why the problem is manifesting itself.   It's common for tubs to exhibit clogs only when draining a filled tub as the rate of flow of water is highest then.  You also might want to put some sealant around the pipes where they exit through the brick.  Very unprofessional.

If these two steps don't work, then it's time to get a plumber.  Get three quotes and pick the guy you like best - not the cheapest guy.