Display entries filtered by one or two related entry fields ordered by "dateUpdated"
If I understand your structure correctly, something like this should work. First grab the ids, merge them (if they don't already exist in the id array), then query for entries based on ids with sort order defined.

{% set programs1 = craft.entries.section('programs1') %}
{% set programIds = craft.entries.section('news').relatedTo(programs1).ids() %}
{% set programs2 = craft.entries.section('programs2') %}
{% set program2Ids = craft.entries.section('news').relatedTo(programs2).ids() %}

{% for id in program2Ids %}
    {% if id not in programIds %}
        {% set programIds = programIds|merge(id) %}
    {% endif %}
{% endfor %}

{% set programEntries = craft.entries.section('news').id(programIds).order(dateUpdated).limit(4) %}

{% for entry in programEntries %}
    {{ entry.title }}
{% endfor %}