We have not had any problems with backing up from running the washing machine for the last 8 months since we bought the unit and now it's backing up all 3 sinks in the kitchen AND it's overflowing in the laundry. I have poured drano down both the kitchen sink where the main drain line is connected and through the washing machine pipe line in the wall with no success. I even took apart the pipes under the sinks to make sure there wasn't something clogged in there. Does this sound like a situation where it's going to need to be snaked? We can't do any of our laundry and we're really frustrated.

I know snaking isn't a problem and you should try it. It sounds like a lint problem, line being put into the draining water because the lint catcher in your washing machine isn't functioning properly.