we charge 100 bucks an hour and minimum 1 hour call, which means this job would cost you likely 120 bucks or soo ( with parts and labour ) It is a stupid company that doesnt look after the smaller jobs as well as the bigger jobs.
Essentially the wye's need to be replaced with T-wyes ( sani-t ) and the laundry machiene should be the bottom p trap. you need to have the vent comin off of this trap arm ( the pipe downstream of the p trap ) Now the wye that has the condensate drain and the softener attached as in the picture, should have an air break before the connection, this can be achieved ( legally ) with an air break fitting, but could also be achieved ( legally but more ghetto ) by drilling a few holes into the dwv pipe beliw the connection, obviouslly being aware of where this condensate and softener drain would direct their water so as not to have the water leaking out of the holes.
an air break is an air break. these fixtures would usually be piped to just above a floor drain using an air gap fitting, or in the cas e of the furnace condensate drain would likely be secured on the cement floor pointing in the direction of a floor drain.
Phone aaround and you should be able to find a plumbing company that isnt so head strong and job shy.