The 2" vent should be adequate to vent the bathroom group.
However...The sink cannot be connected to the 3" pipe. The pipe between a fixture and its vent is called a trap arm and no fixtures can be connected to a trap arm. Wet venting may be an option. You can install a san tee (for trap arm discharge) on the toilet vent for the lav if your area allows wet venting and you do not exceed trap arm max. The 2" part of the wye that is the vent should be rolled so that the takeoff is above the center line of the 3". It must be graded and you must used drainage fittings.