I have previously used a remote heater valve, is this the one that you have?
if so, you will find the four outlets are designed for the standard 5/8 inch heater hose. I am unclear as to where the barbed fitting you are talking about is located.
if the connection you are talking about is the connection to the under-car heater pipes, they are also designed for 5/8 inch heater hose and incorporate a full circumference raised bead.
although not cheap, I would encourage you to look into using silicone hose for your heater installation. Very flexible and durable, be sure to scuff the inside of the hose and use the correct T-bolt clamps.
I don’t know if I touched on your problem. Please give us more information to include location, etc. and we will try to troubleshoot from afar.