We had a plumber come out last week when both our sink drains were clogged. They put "Clobber" down our drain but the next day no real progress. They came back with a dual eel (some sort of snake) and worked that for 1/2 hour. Now four days later the drain to the garbage disposal is clogged (and every time we turn it on there is a leak in the basement) but the other sink is working fine. They said if what they didn't initially do worked they would be back to dig up concrete to replace the pipe or vent or something like this for about $1500 - $2000! EEK! Any thoughts or suggestions

Forget that plumber. Either call another plumber or a drain cleaning company (ie some version of Rotor Rooter). You have a blocked sewer line that needs to be snaked out. Also need to find out why there the leak in the basement is. Could it be that you mean the sewage is coming out of a floor drain in the basement?

Most importantly forget that plumber.