This:
but I would skip that and replace those valves and install the proper ones. Those are Junk with a capital J. Also never a good idea to reuse supply lines like those vinyl ones
Cut all that **** out and glue on at CPVC fitting with MPT (male) or FPT (female) threads. Then thread the appropriate threaded angle stop with 1/4 turn.
There is also a fitting that threads into the angle stop that has an extra outlet to attach your dishwasher line. I does not need its own angle stop. There are also angle stops with two outlets.
Only question I have is what the black lines are...are they the new faucet lines? Why are they facing that direction? Or are you trying to show the ends.
I would have had this done in less time than it is taking to type it except for the run to the hardware/Home Depot/Menards.
Let us know.