While it's OK to stack Tees in some jurisdictions, I wouldn't dump the washer over the kitchen sink drain. You will probably pull the sink trap when the washer discharges if you do. However, it shouldn't be a problem to put the sink tee above the washer tee. If it were me I'd cut the cast iron sink tee flush with the hub it's tied into and drill out the lead joint to remove the remaining piece, then caulk in a PVC adapter. As a homeowner you other option is to cut the Tee out 2" above the hub below it and use a Mission band to convert over to PVC. They make them in a variety of sizes so you should be able to find one to fit. There's a good chance you'll need to file or grind a casting ridge down to get the band to seal but it's no big deal. Keep the trap for the washer box as low as you can to get the longest riser possible. In fact,I'd use an 1 1/2" trap with a 2" x 1 1/2" coupling on the inlet of the trap and then a 2" riser.