The washer drains down a standpipe through a P trap, horizontal about two feet then on a 45 degree drop about one foot to flow into the top of a 45 degree wye branch. Sorry, needed the 45 degree angle to give room to plumb this.

Coming into the other branch of the wye (from the vertical) is a sink drain (already P trapped, about one foot away) with the vent stack heading up from the connection from the sink line.

From the bottom of the to a vent stack, we drop another two feet down and one foot sideways (done in 45 degree drops) to meet the main sewer line in the house.

Would it be code legal, assuming everything else in the lines follow the rules.

Residential, single family, NJ

A Ptrap needs to be at the same height as its Tee connection to a vented drain. Not higher. Therefore, a downward slope (45 degrees) into a Wye is always bad when unvented.

So, the answer to your question is "No, no good, no this will not work."

Where the standpipe P trap is now, it requires a vent. That is one solution.
Otherwise, it has to be a Tee. That is another solution. Not a 45 degree wye branch.

Do you know what a Sanitary Tee is?