The tube you describe as “half blocked” is widely accepted and for the most part works fine without incident. Dishwashers do not use a lot of water these days and water pumped from the unit is pumped at sufficient speed as to make the Dishwasher tailpiece (the half blocked pipe) just fine.
The only other route I can think of is get under the sink and run a new separate p-trap to be somewhere under the sink and run that trap into the drain for the sink somewhere below. It would become a “dedicated” trap. That way you have your 1 1/2″ drain. But it’s totally unwarranted and not needed, you’d be doing work for no reason at all. THink of how often you use your sink and DW at the same time. Not often and as s uch you do get your 1 1/2″ drain once you move beyond the “blocked” part of the tailpiece. Pipes are sized based on water volume and how often they’re used. 1 1/2″ is perfectly acceptable with a DW tailpiece. It’s not taht common to use your sink heavily the same time you’re DW is draining and even if you did you would have some minor slow draining but it’d be fine.
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Well, you COULD put the DW tailpiece on just one sink bowl as its tailpiece, put another regular one on the other sink bowl, then join them before going into the trap. But still it's just totally unnecessary. You're worrying about nothing, you won't notice any noticable difference if you used a regular tailpiece or the dw tailpiece. You might think you will, but any difference is negligable. You're worrying about something thousand of other HO's don't worry about and never complain about because it works fine as it is.
What doyou mean by "real?"
so you found a DW tailpiece w/out the little wall inside is what you're saying?
If your DW's water pump is as energetic as mine, the absence of the diverter may cause the discharge to blow upward into the sink basin.
"Oldfaithful" style if the basket is not in place!
Monitor the results the first several DW cycles!
................Iron Helix