My 1950's house that has a toilet, sink and a shower in the besement recently experienced a sewer line back up. Tree roots were the culprit. I removed the toilet and shower (along with all the paneling) to clean everything. What I discovered was a floor drain under the shower and another drain about 3 ft away. The shower was "plumbed" into the drain away from the floor drain.
The main sewer line is about 12" below floor level. Is it possible that the 2 drains in the floor have p traps ? When I look down the drain opening, I see standing water. I would like to reinstall a shower and use the floor drain directly under the shower.

Floor drains have traps and from you you describe someone installed a shower drain over/into a floor drain creating what's called an indirect drain. They are OK but that is not how we'd do it with new construct. You can reinstall the indirect shower but future back up will be messy either way either with the shower drain or the other floor drain. I'd recommend periodic teatments with copper sulfate. Copper Sulfate Crystals- Pond Algae- Root Killer- Fungicide This will prevent future root issues

What would be the best way to reinstall the shower ? I'm not opposed to busting up my concrete floor to do it the right way. As far as future back ups. (bite your tongue! ) lol I put an outside cleanout in and plan on annual inspections.

I want to make sure I explained myself correctly. I have a traditional floor drain (round cap with holes, bell trap) and there is another drain with a pipe just below floor level about 3 ft away. They had the shower drain pipe running over the other drain with an 90 going down to the pipe that was coming up. Clear as mud now ?

If this were my call I'd bust up the floor, remove the floor drain that had a indirect waste and install a "P" trap and raiser directly under where the shower drain will set, Patch and cement over the trap and the raiser's ready to connect to the shower drain, Good luck, Tom