Your current configuration has a number of code violations. You have a regular Tee connecting the two drains but code requires a baffled tee: Ref IRC-2707.1 & UPC-405.4: Directional fittings are required for continuous wastes from a disposal or Dishwasher (I.E. Wyes, ComboÂs or TeeÂs with baffles). Your Tee is connected by means of slip joints: Ref. IRC-3201.1 & UPC-1002.3: Maximum of one (1) slip joint on the outlet side of a P-trap NOTE: slip joint type P-traps and waste fittings are made to Tube Standard and the single slip joint permitted on the discharge side of the P-trap is the "Trap Adapter" that transitions the slip joint tubing to the Pipe size to match the drain piping in the wall. You can rule out looking for a higher P-trap because P-traps are made to ASTM specification and they are all the same. Increasing the height of the P-trap would increase the water level in the trap above the code maximum of 4". THE POSILBE SOLUTIONS: 1. Install the exact same make and model of disposal and waste kit as was originally installed. 2. Remove the factory supplied ¼ bend on the disposal output and use a Disposal Type" end waste kit. (An ordinary end waste kit has a molded ¼ bend on the cross tube that is intended to be connected to a sink drain tailpiece. A "Disposal Type" end waste kit has a straight cross tube with a flange connection on the input end. The factory supplied ¼ bend in the disposal kit is discarded and the cross tube is connected directly to the disposal port. This keeps the cross tube about 3" to 4" higher. The disposal type end waste kit comes with the code required baffled Tee.) 3. Open the wall and lower the elevation of the waste arm. 4. If you are under the IRC and if the waste arm is a 2" pipe you could cut the trap adapter off the waste arm then install a Wye with a trap adapter on the end and the side port, then install separate traps from each sink. (Note: It must be a 2" waste arm because if you install separate traps the load must be computed as separate sinks with a 3DFU value for each trap. Under the IRC the maximum permissible load on an 1-1/2" line is 3DFU however if it is a 2" line the maximum load is 6DFU and separate traps would be permitted. (Note-The UPC prohibits connecting two traps to a common waste arm)

#1 reason for not haveing two is that there isn't enough room under most sinks. Among all the other reasons for not haveing two,the best is because one is enough.

If the washer waste water dumps into the utility sink then I would replace the utility sink and p trap first.

Thanks for the responses. I know brass is on trend now, but I've lived with shiny brass fixtures all over my house for so long I vowed when it was time to update the brass had to go. The more I think about it, though maybe I should at least look at the new brass faucets. It would solve the p-trap dilemma. If I do decide to go with chrome I'll look into Rub N Buff, I've never heard of it.