Simulated handicap bathroom drain mashup

The only thing I know for sure is that sh*t runs downhill, it's the little things that have stumped me. I'm trying to save some room under a sink in a bathroom remodel, and the guy at the plumbing store put this contraption together - but neither of us are plumbers, and he said to "check with a licenced plumber, I just sell the stuff". This is my check.

Basically, I'm using an offset drain with a slight extension and hiding the p-trap in the stud cavity, and I'll cut an access hatch under the sink. Can I have a horizontal, or close to horizontal, drain line like shown with the p-trap tucked away like this or am I violating a rule of physics/code?

I took 2 pictures, one from the side, and one from the front - it's easier than trying to write it all out.

trap

I would put the trap outside the wall but parallel to it the way yours is. Putting it in the wall, even with access and especially with that trap, is creating a potentially difficult situation some time in the future when the drain is stopped up. And, keep this site in mind when you find out your sink does not drain properly because you used that drain system and design.

Ok, I'm slightly scared now.

Putting it outside the wall is possible, and probably smarter. So what you're saying is that after the trap I'll have a 90 turning it into the wall, then another 90 to turn it parallel to the wall and continue to the stack.

What do you mean by "especially with that trap"? I thought this was a standard p-trap with cleanout? Is this a bad trap or something - should I be installing somethign different?

Also, by "drain properly" - will it just drain slower, or louder, or what?

drain

I "abhor" using that kind of traps for sinks. I prefer, i.e. have ALWAYS used, tubular traps with slip nut connections. It will drain poorly because you have a lot of air in the pipe between the sink and the trap. Even though you sink has a overflow, which usually vents the air, in your case, water running into the drain is going to "trap" it and until it escapes somehow the sink will either NOT drain or will drain slowly. The "second" elbow outside the wall will be the one in the trap pointing downward and the "U" bend will be turned laterally against the wall. doing it this way will eliminate that short extension piece which would create a "wobbly" connection if left in place.