No, there's a few issues with your diagram.
First, as background, every fixture needs a vent within one trap diameter of fall from the fixture trap outlet. There's also a length limit between the trap and the vent, which is 42" for a 1-1/2" trap and 60" for a 2" trap. A WC doesn't have the fall limit, but the length limit, including vertical drain portions, is 72" from the closet flange to the vent.
Now, the way wet venting works is that instead of having a vertical dry vent takeoff as your vent, the junction with another dry vented drain is the vent for your fixture. So if we delete the washing machine and the WC from your diagram, the lavatory drain could be the wet vent for the shower, as long as the shower trap arm, from the 2" trap outlet to the wye where the lavatory drain joins, is under 2" of fall and 60" of length.
Similarly, if we delete the shower and the washing machine, the same idea could work for the lavatory to wet vent the WC (and in this case the lavatory needs a 2" dry vent as you show, since WCs always require a 2" vent). Except I would guess from your drawing that the distance from the closet flange, down to the closet bend and the horizontally to where the lavatory drain joins is over 6'. If I'm mistaken, then that would work for just the dry vented lav and the wet vented WC.
However, this type of wet venting for a bathroom has a couple additional rules your diagram doesn't comply with. First, you have to vent each trap arm before it joins another trap arm. Ignoring the washing machine, starting at the WC you have the shower join first, and then the lav join. You can't join the two unvented trap arms; you'd need the lav drain to join the shower first, and then they both join the WC; or the lav join the WC first, and the shower joins.
Except for another rule, which is that the WC has to be last wet vented fixture, so that second order isn't an option. Starting at the lav, it first must join the shower, then join the WC, if you want the lav to wet vent both the shower and the WC.
And lastly, the wet vent has to carry only bathroom fixtures. So you can't bring the dry vented laundry drain into the middle of the bathroom group. The laundry drain needs to join the branch drain downstream of all the wet vented fixtures, including the lavatory drain providing the vent.
One way to fix all the above problems would be to add a 2" dry vent to the shower trap arm before it joins the WC. Then the shower would be wet venting the WC, and that's it for wet venting. [Also the lav vent could be only 1-1/2" in this case, as it's not involved in the WC venting.] But I'm guessing that's not a viable option given the shape of the shower you've drawn, you won't have any solid walls around the shower near where the drain is currently shown.
Cheers, Wayne