I thought one of the regular licensed plumbers would have answered this with a better answer than this, but let me share what I have learned from this board in some of the past answers. Some of what I give you may not be 100% accurate, and local code may dictate what can or can't be done. As I understand it, an "S" trap is not legal in any code. Air admitance valves, aka Studor or AAV, work, but many plumbers don't like them because of possible failure. They can not be the sole vent in the system, you must be vented to the outside. In other words, it can't be the sole vent. If you are tying into the stack, the connection must be 6" above the highest fixture in the system, so I don't think you can do the wet vent as you described. Sorry to be a bit vague, but you asked a good question and it deserves an answer. Check with the local authorities on the legality of what you are trying to do. They can tell you for sure and possibly offer some other ways to do the job.