JSFiddle - React, Tailwind, and code Playground

HTML

<!-- First parent -->
P <input type="radio" name="parent_1" data-smth="parent_1" />
<!-- Children of this one -->
<input type="radio" name="child" data-parent="parent_1" />
<input type="radio" name="child" data-parent="parent_1" />
<input type="radio" name="child" data-parent="parent_1" />
<!-- Second parent -->
P <input type="radio" name="parent_1" data-smth="parent_2" />
<!-- Children of this one -->
<input type="radio" name="child" data-parent="parent_2" />
<input type="radio" name="child" data-parent="parent_2" />
<input type="radio" name="child" data-parent="parent_2" />
<!-- Third parent -->
P <input type="radio" name="parent_1" data-smth="parent_3" />
<!-- Children of this one -->
<input type="radio" name="child" data-parent="parent_3" />
<input type="radio" name="child" data-parent="parent_3" />
<input type="radio" name="child" data-parent="parent_3" />

JavaScript

$(function () {
    $(document).on('click', '[data-smth]', function () {
        $('[data-parent="' + $(this).attr('data-smth') + '"]:first').prop("checked", true);
    })

    $(document).on('click', '[data-parent]', function () {
        $('[data-smth="' + $(this).attr('data-parent') + '"]').prop("checked", true);
    })
})