Lee, I'm an Electrican and this is a strange thing. This may be a far shot but heres my guess.
When your running the washer it may be using a lot of your hot water suply, Depending on your dishwasher,the new ones have a heating element in them so when the water isnt hot it kicks on. so it may have nothing to do with the washer itself. Just not enough hot water. Looks like you need to add 5 circuits to be up to code. Tim