I need to remove my laundry sink and alter the plumbing to adapt to a Dishwasher and Washing Machine. As the drain is in the middle - how can I do this with out moving the Drain (we rent and need to replace the sink if we move out).

Code requires the washing machine to connect at its first branch to a 3" pipe and it can not wash by a toilet. If your pipes are not sized correctly you may well get constant stoppages and overflows, and it could syphon the water from your toilet bowl.