Hi Guys: Bones is wrong about the washing machine vent....sorry bones
All fixtures with a trap require a separate vent.. there area some exceptions in that we can wet vent
certain fixtures, but these fixtures are stilll considered vented as they are using a vent from another fixture to be vented... complicated to explain, but all fixtures require a vent! Washing machines cannot be wet vented.
If you did not individually vent the washing machine by running it up and connecting it into the kitchen sink vent then when the kitchen sink waste passed the washing machine ptrap it could be siphoned of its water or bubble/gurgle, etc... both allowing sewer gasses to enter into the home... a health hazard no doubt
Anyway, you can cut into the 2" kitchen sink drain pipe and install a 2" sanitary tee fitting (using shielded clamps... see picture), install an 1.5" vent and a 2" ptrap with a 30" standpipe. The 1.5" vent will need to run upstairs and connect into the kitchen sink vent at 48" off the finish floor (on 1st floor). If that proves difficult then you want to look around the basement to see if there are any other vents that you can connect into.
Worst case, you may be able to install an automatic air vent (AAV
... see picture #2) in place of running the vent pipe upstairs. Be clear that the AAV may not be code legal in your area and that these vents can fail (mechanical parts) and will most likely need to be replaced down the road. These vents cannot be installed inside a wall unless there is an access panel installed for future access.
Check out the pic. Below. I did not include the two 90s you mentioned and I guessed on a couple things. Let me know if I am in the park anyway.