sink drain in new kitchen

Hi--we have a deep undermount sink--the strainer basket hangs down lower than before. I have a double bowl sink that would need some sort of "T" fitting, and I need a "Y" fitting for the dishwasher. When I stick these things together on top of the trap, I have run out of vertical space. The trap is lower than the drain stub on the wall.

Can I run the dishwasher "Y" horizontally, as long as the output faces towards the drain? Can the "Y" be put horizontally between the trap and the wall?

It can be horizontal between the two sinks, but not between the trap and the wall.