My laundry room is in my basement and currently the discharge hose just dumps into the sanitary tub/sink. I'd like to change this and create a separate drain pipe for the washing machine. Its all PVC plumbing, with a 2 inch drain line right next to the washing machine which the sink currently connects to. Can I just cut that drain line, insert a T and run my plumbing for the washing machine? Seems very simple and easy to do, am I missing something? I've attached a crude drawing to show what I'm talking about. The left side of the drawing is what currently exists. The right side is what I'm looking to create.
What you have is the right idea. I'm not sure of the exact minimum dimensions needed but I think it is a minimum of 2 inch diameter line for the entire washing machine drain assembly and the vertical end up to where the hose connects in has to be at least 18 inches above where the assembly tees into the main drain.
You may not splice more hose onto what came with the washing machine to reach the mouth of the drain pipe or to reach anything else, unless the washing machine instructions specifically permit that.
The hose must fit loosely into the drain pipe.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.