Double Kitchen

How to unclog my kitchen sink when double elimination outbreaks of water for sinks in both?
I a big problem with my sink of the kitchen. This is a double sink and one side is a provision. The other side has no provision. The two parties do not go at all – unless I dig the heck out of them. When I run the disposal, to the removal of water from the sink drain, but then pulled right into the second sink. After disabling provision, the two sides boiled over again. I tried Liquid Plummer, tips, etc. My husband tried to snake it. What to do?
You can try to remove the trap and operation of a snake through it. If this is not going to the cellar. In the area under the sink, Choose a drainage tube with a nut on their own. The United Nations, he saw the wind and try from there.