Hi Brakerbick...
If
wet venting (would need to ask a local inspector) is allowed in your area you may be able to chip the concrete floor up over to the 2" sink drain underground (all pipes are supposed to be a minimum of 2" underground) and connect the shower drain pipe into the sink drain pipe.
Here, you will expose about 12-18" of the sink drain pipe and then you will use a reciprocating saw with a bi-metal blade to cut out SAY 12" of the 2" cast iron pipe and install a 2" PVC wye fitting. You will need special
2" cast iron x 2" PVC shielded transition clamps (see picture) to make change from cast iron to the PVC wye fitting for the tub. Then you will lay out the pipe/wye fitting as drawn below, add a 1/2" to the overall length (in this case, 12.5") and then lay that out on the cast iron pipe and cut the pipe. Then you will install the clamps, FLIP the rubbers back on themselves and then drop the pipe/wye fitting into place and then FLIP the rubber sleeves back to join the pipe and then slide the SS clamps over the rubber sleeves and tighten all up. You can now run a PTRAP over to the tub area as long as the trap won't be more than 6 feet away from the sink drain.
If tub ptrap is more than 6 feet away then you will need to add an 1.5" vent just before the tub ptrap and that vent will need to connect into the sink vent at about 48" off the finish floor... ok?
If wet venting is not allowed in your area then you will simply need to run the individual vent as mentioned already.
You will not cement the dapout box. Instead you will use this space to connect the PTRAP to the
tub waste and overflow assembly from the tub... see picture You will connect to this tub waste and overflow assembly using an
1.5" PVC desanco fitting (compression x PVC fitting) or an
1.5" PVC female adapter and install that into the PVC ptrap.
Let me know if need more here...
MARK