Plumbing drawing for 1/2 bath

Can someone take a look at the attached drawing and tell me if I am a hack on this? I have no stack on that side of the house and I was reading our code here and we can vent using a AAV as long as its accessible and above 6" of the highest drain. I want to add this 1/2 bath to an area near our kitchen. I have no way to vent this the best way so I am told this is the next best thing. I have a Studor vent so its not one of those trailer home types. Also, is the vent in the right line for these to vent properly?

I believe the venting is definitely not correct, but others will have to help. I barely know anything. And I don't want to start throwing ideas out there about what might be wrong if my ideas are wrong. That would just add to the confusion.

But we need to know the distance from the sink trap and toilet drain to the stack. There is a maximum distance allowed based on pipe size that a vent can be from the trap for a fixture.

As shown you are way off on venting. As stated above we need a lot more information. You could in theory vent the lav sink and wet vent the toilet with the lav. Why is it you can't go through the roof? Because you don't have to?

Vent

Take the 1 1/2" line from the lav. straight up 6" above the flood level rim of the sink..90 over to the 2" vent and you'll ok as long as you vent that 2" through the roof or tie into another vent in the attic.

Hold on a second. I think I may have confused all of you. Sorry.

I can not get to the attic for this application because I can not; not because I won't. There is no run for me at all, unless I vent out the side of the house and make my way up the outside wall and back into the attic and then over 20' to the stack on the other side of the house. This is why I asked about using a 2" AAV which is allowed here in Ohio.

Knowns: My main stack is cast iron and is on the est side of my 1920's 2 story bungalow. I do not have balloon framing, and I can not fit a pipe of even 2" all the way up to my attic. This is a lav I am building that is under some stairs on my first floor. The 1920's builder used 2x4's in the wrong direction for framing up my stairs, so all my walls are 2" deep; not 4" deep so that is another reason I can not get up in the walls.

So. A while back I tor up the basement (see other post about that) where I had a drain in the floor in the basement directly under this room. Distance was 7' from the top of the floor drain, and the floor above. I opened this clay drain up, cut a 3' section out removing the trap, and put in a Fernco 3" PVC to 4" Clay no hub and repaired that pipe. I elbowed out to the floor, poured concrete and I now have a section of 3" PVC sticking out of the floor directly below the room where I want this to go. Again, this sits almost 15-20feet from the stack on the other side of the house. My kitchen is connected to this clay pipe i dug up and I found that it was not vented at all, and works fine. Its 2" galvanized pipe that connects to that underground drain.

What I was asking was if I was able to use an AAV to vent both the 1.5" lav sink and 3" toilet. This drawing is assuming that the height of the 3" pipe was 7' tall and the 2" pipe is 5' from the 45deg fitting.

What some of you are suggesting is that I should vent the lav, but don't I need to vent the toilet too?