I want to install a utility sink in my laundry room utilizing the same drain/vent Name:  Vent 1.jpg
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Size:  37.6 KBName:  vent 2.JPG
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Size:  89.8 KBas what the washing machine uses now.

Current setup: Washing machine
enters into a drain, goes through a p-trap, then that connects to the drain/vent pipe from the left side. There is also a connecting drain pipe from an upstairs bathroom that you could see near the floor (in the picture) that taps into the drain/vent.

What I want to do: I want to install a sink on the left side also and run the drain along side the drywall and turn it 180 degrees and enter the same drain/vent used for the washing machine from the right side. I figured turning a pipe 180 degrees isn't a problem, so long as I have enough slope in the drain pipe. (But if there's an easier way, I'm open to ideas)

Problem: In a perfect world, I would be able to use a double Y connection on the drain/vent (one for the washer and one for the dryer), however, the current connection for the washer is to high on the vent, so I would need to bring the utility sinks
connection below the connection of the washer on that same drain/vent. Does this cause a "venting issue"? Any other ideas? Thanks!