Need help for ice maker line splitter to be used for coffee maker
The problem with your idea is the risk of damage of the line and associated leakage.

While ice makers use thin copper or plastic lines, they are permanently attached and not handled once installed. The valve that controls the filling is built into the ice maker, and is automatic.

A similar approach to your coffee maker would require that you have a fixed mounting for the valve that is substantial and protects the line and attachment from rough handling. There are such systems used as pot fillers, like this one



These are permanently mounted on a wall very close to the point you fill pots, such as a stove.  The risk is spilling water in an area with no drain. These units are usually installed with standard plumbing (copper, pex, etc.), not lightweight tubing, although adapters probably could be used to accommodate small tubing.

While there are small plastic valves that are used on things like water jugs, these are also intended for fixed mounts of the valve.