Sewer line branches under living room where rooter man thinks there is fracture in drain line. Can I avoid tearing up floor by routing lines down outside of house (laundry and kitchen to one line; adjacent bathrooms have their own line to sewer, connect all to main sewer line)? Don't want to tear up the slab floor.

Rerooting outside will still require some slab busting up. Get a real plumber, a licensed plumber should have access to a SeeSnake camera to pin point the exact location and problem. There should be not guess work with this. The whole should be about the same size or smaller than any rerooting hole.

Hi John,
I had a OP with the same prob lem yesterday. His were branches just like yours. His question was can I get this done without tearing up the slab too much.
Bob nailed it with his answer and here's the answer I gave to the OP.

If they're on a outside wall there is a possibility that the branches can be brought out side and run around the house to tie back to your sewer.
I did that with my own sink and washer. The vents will stay in place as usual and not be disturbed.
Good luck, Tom

Get video inspection first. Pipes do not collapse like that under slab. See the damage first before you proceed with this type of work.