Can I run a tub drain into the 1 1/2 vent pipe and use a loop vent? or would I have to open up the floor and install a drain in the existing drain and than install a loop vent?

Which code has Wisconsin adopted? Wet evnts are allowed by some but not by others. By loop vent do you mean a island vent, aka Chicago vent? Why would you need to vent a connection to a vent? Or am I reading this wrong?

It's been over 50n years since I left Beloit so the codes have changed but if remember correctly If there are fixtures that are using this vent you will have to run vent off the laundry tray trap.
What's with the island vent? Is the laundry tray setting out in the middle of the room? A better way would be to install a AAV ( air admittance valve) just downstream from the trap. (see image) Good luck, Tom