Good morning Franc,oise,

A blockage is the simplest job a plumber faces. In point of fact, in our area, the men that work for sewer cleaning companys are for the most part not licensed plumbers. The work's so simple they don't have to be. Having said that, let's analyze your problem. I need to know if you're on city sewer or a septic tank. (This question's important.) If you're on a septic tank you will have a separate line from the sink and laundry to a grease trap before it goes into the septic tank. (My hunch tells me that this might be the case.) But if you're on city sewer you know the lines are clear from the washer to the sink so the blockage must be downstream from the sink so why cut up the wall behind the washer? I hate to knock another plumber but your man looks like he doesn't have a handle on the situation at all.
First of all is he using a Ridgid K-60 sewer machine or equivalent with a spade tip to start with? Is he snaking out the correct vent from the roof? It should be the kitchen vent. Is he putting out enough cable to reach the clog? In a difficult case I open up the clean out and put enough cable down the vent to reach it. Then I let a sink full of water go and see if it passes the clean out. Let me know about the septic tank. A clogged grease trap that needs to be pumped and cleaned would answer all the questions about why he's having such a hard time. You shouldn't have to dig up and reroute any lines for a blockage unless the line has completely collapsed, in which case he would know if he brought back dirt on his auger. Keep me in the loop on this. Yeah got me curious! Regards, Tom