You have a number of issues, and you should have a plan to sort them all out before you make any changes.
One basic issue that I'm not sure if you're aware of of is that for a separately trapped fixture like the shower or a sink, the drain between the trap and the vent takeoff (the trap arm) has to be horizontal, is limited in length, and can't fall more than one pipe diameter. Also, you need to vent each fixture drain before combining drains (or, in the case of wet venting, as you combine drains).
1) WC--once you fix the horizontal 2" vent in the floor joist area (replace two 90s with two 45s), this is properly vented.
2) Lavatory--is the lavatory trap properly vented per the above description? If so, there should be a 1-1/2" vent taken off a san-tee (most likely) in the bathroom above. Your drain routing is fine, although it may be useful to use the lav drain to wet vent the shower, which would require rerouting the lav drain. [And if you end up changing the lav drain, using a single 45 to hit the stack wye would be more elegant than the LT90 and the combo.]
3) Shower--is there a trap between the joists that is hidden? If so, does it have a vent takeoff?
If not, the easiest way to vent the shower would be to lower its trap to below the floor joists, and to make use of the WC or lav vent via wet venting. To do that, the shower drain needs to stay separate from other drains until it joins the lavatory drain via a flat wye (horizontal wet venting), or until it hits the 2" vertical WC vent via a san-tee (vertical wet venting). With a 2" drain, at a perfect slope of 1/4" per foot, the shower trap arm can be up to 8' long.
4) Kitchen sink--you can't combine the drain with an unvented drain. So it is going to have to travel to the 3" stack on its own (unless you choose to individually dry vent the shower drain with in the joist system.) If you remove the combo where the shower drain comes in, you can leave the reast of the kitchen sink rain piping. Except that the vertical jog would be better done with two 45s, rather than two 90s.
Cheers, Wayne