Hi Hr_Veedu,
If the dishwasher calls for 3/8", I'd not reduce it to 1/4" Using geometry, 1/4" supplies 1/2 the water of 3/8". (Actually less because they are measured OD and the wall thickness is the same.)
Or did I understand backwards- The dishwasher wants 1/4" and you have 3/8"?
If so, reducing fittings for compression are available in straight and tee configurations. I think places like Home Depot or Lowes should have some. McMaster Carr and Grainger absolutely have them. Plumbing wholesalers have them.
Hot water to an ice maker might not be a great idea.
At minimum I'd suspect, if the ice maker draws enough water to receive hot, the cubes will be aerated. The freeze cycle will be longer, too.
And, do you want to introduce steam into the freezer compartment? It will make the evaporator ice up quickly. (And the walls and door gasket.) I wonder, too, if hot will damage the fill solenoid.
How hard would it be to swing the tap over to the cold supply for the sink faucet? Or, perhaps take it to the supply in the basemen tor crawl space? Just a thought...
Paul