Based on the first drawing, you had the waste from the lavs coming into a fixture cross that was supposed to be venting the washer. In that drawing, I would have raised the washer santee higher to make sure that the washer was vented higher then the incoming lav.
The double lav on the right of the first drawing was correct with the fixture cross for just the two lavs.
Hackney suggests putting a santee above the washer santee and wet venting the lav over the washer.
Since it is a lav, which normally could use 1.25" waste, you gain your two pipe sizes by dropping it into a 2" wet vent.
If it had been a laundry sink, which requires 2" waste, then it wouldn't be considered a wet vent in some places. Washington no longer allows a laundry sink wet vent over a washer, but the lav over the washer should be fine, since it's rated as a smaller fixture. hj says that Arizona is one place that allows that though for a "laundry sink".
Just so you know, the State doesn't consider us a journeyman plumber until we have worked 6,000 under an apprenticeship, and have passed the test for journeyman. I'm sure all of this seems simple, but the fittings can be arranged many different ways with many different results.
You're getting there though with these drawings. Pretty soon you will have the right one.