I cut opened a 4" wide trench about 8' long to pass a 1/2" PVC pipe from the
wall to a kitchen island. Just as I was about to close off the trench my
wife asked if it's possible to have a sink in the island...

The island is about 7' from the wall, the trench is 8' long to that wall.
The nearest drain line that is open and accessible is the utility bath room
which I do have the slab cut open and the 3" drain exposed.

I am contemplating running a 2" PVC drain from the island to the wall (this
is not a problem as the trench is already cut and open), now once I am there
at the wall, the utility bath drain is 7 feet away and the pipe has to make
a turn to the right about 22 degrees.

So my challenges a

Can I really pass a 2" PVC pipe under 7' of slab? I don't want to cut the
slab open. It's mostly sand under the slab down here in Miami, If I do, I
have to do it from the utility bath end and hope that the pipe will appear
at the end of the trench where I can put in a 22" elbow. The problem I see
is 7' is a long distance to bridge, and since I am starting from the utility
bath end (downstream) it will be tricky to maintain the proper slope as I
get the pipe through.

Even if this all work, the run will be 8' + 7' = 15' to the tie in to the
main line and no venting. I could vent the pipe at the wall and run a 2"
vent up to the attic and tie in with another vent stack but even that is not
to code as code calls for 5' maximum vent distance. Someone told me I could
use a studovent? (spelling) how does that work? Does it apply in my
situation?

Thanks in advance,

MC