Okay, Basically. The sunk-in shower is obviously lower than the bath tub. And I wish to connect the new drain from the tub to the existing 2" drain from the shower. My question is: How would I go about venting (if needed) and connecting the new tub that is 4' away from the existing drain, Without, having any suction or backflow to the P-trap of the shower when we drain the bathtub?

The ideal way is to open the floor and simply move the trap to the proper place for the tub. 2" can travel up to 8 feet total and 1 1/2" can travel 5 feet from the vent. You probably have a 2" line, maintain that with a 2" trap and 1 1/2" riser

Thanks Doug.