double sinks

The components consists of a double sink, garbage disposal and a dishwasher that drains into the garbage disposal. At the joint circled in the second picture the drain keeps on clogging and water/particles are forced through the pipe. The drain pipes are taken apart and the blockage is cleared...

Is the set up/procedure for planning to upgrade my master bath Vanity from a single sink to a double the exact same as the double sink plumbing for a dbl kitchen sink? The current sink is mostly in the middle of a huge vanity and the new ones will be spaced out evenly across the whole thing...