Help with planning drains/vents (air admittance valves) for bathroom shower addition

Hi,

After reading these forum posts I decided to take on the task of adding a shower to my downstairs bathroom, and I would appreciate any help you can give before i start (and probably mess something up, lol). The bathroom was added by the previous owners inside what used to be the garage so it is far away from any existing vents. Finding out that I do not need a permit for the project and demolishing the old room, the existing pluming looks like this (i hope you can figure out my diagram, I am new to this):



I am pretty sure that the 3x3x1.5 90 degree elbow under the toilet is not up code. Also, in this configuration we had some issues with the toilet backing up a lot.

I hope i have the code correct. My township uses the Pennsylvania Uniform Construction Code which directs me to the ICC, so I am pretty sure that both wet venting and air admittance valves are allowed.

As it would be very hard to run a vent out of the house in this location my plan is to modify the plumbing to look like this:
(shower being opposite corner of the toilet in the picture)


The new AAV will be in the new wall with an access grill on it

My questions regarding this new plan are:

Am i ok with code?

Do i need to have a second AAV? Could i eliminate either the sink or shower vent?

Would this help alleviate the issues we had with the toilet backing up by getting rid of the 3x3x1.5 90 degree elbow under the toilet, or is there something else i am not considering?

Is there a simpler way for me to run these drains/vents?

I appreciate any help anyone can give, thanks!

I'm no fan of AAV's but..what you drew is fine providing AAV's are allowed in your jurisdiction.
You do need both vents.

I did not expect such a easy answer, lol. I guess i did my homework!

I will probably take a picture of the pipes when i dry fit them to triple check my work.

Thanks again for everyone who contributes to this forum, I definitely utilized a lot of great information from here!

If you dry fit, remember to leave each section long. If you don't, you'll come up short. When dry, the pipes won't go all of the way into the sockets, but they will when it is time to glue everything up.