Moving a master bathroom into a spare bedroom
I am currently converting a second floor spare bedroom off the master bedroom into a new master bathroom. The new bathroom is about 10x10 plus a water closet. There will be a double vanity along the north wall, (a load bearing wall), then a whirlpool tub and shower along the adjacent (west) wall and then into the water closet on the third (south) wall. As it used to be a bedroom, I have to bring plumbing in. The main stack is about 16' in a straight line (east) from the new toilet. My original layout for the plumbing was to start at the double vanity with 1 1/2" ABS, drop down under the floor and cut across the room straight to the toilet. There would be a 2" vent about 10' from the double vanity and about 2' before the toilet. Another line would start at the tub, connect into the shower, with a 2" vent in between. At the shower, it would run east about 6' though the joists and tee into the 1 1/2" run from the sinks. Because of the joist layout, the toilet has to make a 90 to the right (south) and then an immediate 90 to the left (east) to run the 16' feet to the main 4" stack. I was planning on using a 3"x3"x2" tee that would be at a 90 to the toilet so that the sinks, tub, and shower could all tie into the 3" toilet drain.
I have a feeling that there are at least a couple of problems with this layout. The 2" vent for the toilet and sinks seems too far away from the sinks. I think that there should be a vent in between the two sinks but in my situation that is difficult as there used to be a window above where the sinks will go so there is a 2x10 header. I do have attic access. Is a 3x3x2 tee acceptable at a toilet?
Any help would be really greatly appreciated.