Seeking advice on second story laundry room

first of all, a washing machine requires a 2" drainline, what you currently have is 11/2"
also that cheater vent should have been above the flood level of the fixture
each fixture requires a vent connection one way or another. cheater vents are legal however you must meet certain codes/criteria and their performance are not always ideal

PS, water you can run however you want so long as its not in the outside wall. Drains are a different story, there are many different codes that will come into play

My response to this would be - take the 15 -20 minutes and go into your City Permit Department and just ask the inspector. The plumbing code is slightly different depending on where you live, and each city / district / province has slightly different flavors. There is also the benefit to discussing it with the person that would be approving the inspection anyways. It's free to go in and talk to them (Generally they are open for home owners for the first hour of operation (after that they are in the field) and you generally do not need to book ahead of time (just show up at the counter).
Normally I am all for the questions in this forum, but this comes down to so many factors in this case (distance to drains, fitting connections, wet and dry vents, outside and inside walls etc etc) that it’s not going to be just a single “Do this one item as per code X”.
I say this from experience. I had re-done all of my plumbing but the plumbing code (I'm an electrical engineer) leaves so much interpretation (at least to me it seemed – probably night and day to a pipe fitter!). In terms of venting, there are "wet venting" options that could be considered (again you're inspector would know right away - just show up with some pictures and sketches as you have above. They will also give guidance on rules such as the minimum and maximum distance of the drain line from the floor for the washing machine. I assume you’re going to pull a permit, and this service is part of paying that fee (otherwise what else are you paying for but for him to come and just waste both of your time with your first attempt with no input from him).
This saved me tons of time. And not only that - but I wanted a drain line that tied into the "Wet Vent" - but it needed to be within 3 feet of the vent. I wanted to go 4.5 feet and discussed it with the inspector which he allowed to do based on my circumstance (the rules are there as guidelines and provided you have good reason and are not WAY outside what the purpose is (such as putting things like S traps instead of P traps) they can sometimes be flexible.

hitman_24 wrote: ↑first of all, a washing machine requires a 2" drainline, what you currently have is 11/2"
also that cheater vent should have been above the flood level of the fixture
each fixture requires a vent connection one way or another. cheater vents are legal however you must meet certain codes/criteria and their performance are not always ideal

PS, water you can run however you want so long as its not in the outside wall. Drains are a different story, there are many different codes that will come into play

Thanks, Ill take a closer look at the diameter of that pipe. The pvc actually attaches to the old galvanized drain just a few inches below the floor via a rubber sleeve. If that pipe is also 1.5" are you saying that the current location is impossible to use unless I replace that entire pipe?