Is there a way to group players by color-coding their names?

I want to set up a local Minecraft server (e.g. 'local' as in 'my hometown') for parents and kids I know.

I would like to be able to put the parents in one group and kids in another by color-coding their names. (e.g. parents names in 'yellow', kids names in 'red').

Is there a way to do this at all?

There is a way to do this in Vanilla Minecraft, using the Scoreboard feature. You don't even need to create an actual score to track. Just use commands along the lines of

/scoreboard teams add greenteam
/scoreboard teams add redteam
/scoreboard teams add blueteam
/scoreboard teams option greenteam color green
/scoreboard teams option redteam color red
/scoreboard teams option blueteam color blue

This example creates three rather unimaginatively-named teams, and gives each team its own color. Feel free to choose the names of the teams however you want. Then use

/scoreboard teams join <team> <player>

to put a given person on a given team. This will make their name take on the team's color in chat, above their head, and on the Tab menu of all currently-signed-in players.

While the team mechanics can be used to do things like team-based disabling of friendly fire and the like, the default settings are for a player's team to have no direct, actual effects on gameplay.