On occasion when I see water standing in my right sink where the garbage disposal is, I assume something is in the disposal and while running water turn it on and clear it out. In that circumstance waste then goes into the opposite sink. This has gradually gotten worse and now both sinks fill up and it takes hours for them to empty. The garbage disposall only makes it worse by filling up the sinks more. I've read responses to other similar questions, but they seem so drastic. Isn't there some remedy I can use to attempt to unclog without trying to become an amateur plumber? Non-caustic of course. Could it be the disposal, the connection from the dishwasher to the disposal, or.. Thanks for any help.

Sorry Gabbey,

There is no magic repair when it comes to blockages. However, I'm going to give you some options. The reason the other tub fills when you run the disposal is that the disposals table acts like a centrifugal pump.
Now, back to your clog. Your stoppage's in the lateral drain line in the wall.
(good) Tonight pour a 1/2 gallon of bleach down the drain and let it set overnight. Next morning, (if the water's gone down) flush the line out with a few pans of boiling water.
(best) Remove the "J" bend from the trap and send a snake up into the wall. You will hit a elbo about 8 inches in but work your way around it and you'll only need to put out 6 feet more. Flush with boiling water.
Good luck, Tom

Tom's bleach ideas is good and it does work. However, I have a favorite mix that creates a bit more action and can also knock open many blockages. Mix 1/2 cup salt with 1/2 cup baking soda. Mix dry and pour into the drain, not the one with the disposal. Then add a cup of vinegar and also to sit over night. Flush the next day with severasl gallons of very hot/boiling water. The foaming action caused by the vinegar/baking soda not only disolves the junk but it creates a physical movement within the pipe. If it works for you try it again the next day on the side with the disposal. Both approaches work pretty well.