I used to hate back to back lavs..Try plunging one side holding the other, still wont drain?Go to roof vent if possible and if its a small stack blow down it ,feel pressure if so run your small cable down stack,,but what if they go into 3 or 4 inch main vent.Drop a penny or pebble down the stack if it splashes ,take a stick of 1/2 inch pvc drop it down stack the stoppage is just above toilet and below where both lavs connect its easy to knock most stoppages out , .Or do it the messy way cut pipe close to wall on one side look in pipe with small light and fish small cable thru arm, its messy as hell this way. .I like the roof better its alot cleaner same with kitchen sinks when my 50ft 1/4 inch cable thru trap wont reach the stoppage then I take my old my tana apart and run 100ft down stack if necessary (I like to run water to wash mess off the cable before putting it back in drum or reel).I use a gorlitz mini for most inside jobs it carrys 50 ft of 1/4 inch cable .I usually cut the coil off the end and drop cable thru strainer alot of plumbers argue about which machine is best I say its not the machine its the man using it .Drain cleaning kept me going when new work faded out and I usually work for other plumbers now all my reg customers are dying off , taking stuff they dont want.the fellows that give me the most work usually get use of my camera and locator for free we swap work around ( Im not as good as I once was but good once as I ever was)