I would make the trap arm(horiz portion on the kitchen sink) 2". Max run of that horiz is, I think 6'. The laundry sink below is not vented. As drawn you have a "wet vent", meaning you are using the kitchen sink waste line as a vent for the washer. You could move the washer trap assembly off to either side of the kit. Sink drain. From there you can tie into the laundry sink vent or run a vert line up along side the kitchen sink drain and tie it in to ks vent above its trap arm.

I run ABS. PVC is frequently used as well. Local code may make the call for you

Hi Jackfre! thanks for offering your suggestions. Unfortunately, i drew the picture wrong. I have attached the correct picture.

Thanks,
Jesse