Adding utility sink and washing machine drain to existing drain from floor above with AAV

[vaulterben]

I'm trying to relocate my washer and add a utility sink in my basement. The only drain option I can think of is to use the existing 2" drain pipe from the kitchen sink, with dishwasher on the floor directly above. I have drawn up the following two options utilizing an AAV. Is this against code, what do I need to change? I am in Boise, ID and permitted to use AAV but want to ensure I vent properly and am ok to drain into the existing drain from above on the first floor. Open to any and all other options. The existing laundry drain is located 25 feet away near the main stack.