Query for multiple date ranges on a date field
You can use two queries, each for each range, and then merge them like this:
{% set firstRange = craft.entries({fieldHandle: ['and', '&gt;= '~date1FirstDay, '&lt; '~ date1LastDay]}) %}
{% set secondRange = craft.entries({fieldHandle: ['and', '&gt;= '~date2FirstDay, '&lt; '~ date2LastDay]}) %}

{% set entries = firstRange |merge(secondRange) %}

This is the way to do it. Also you should query for the ids, and then merge those, and then query by id.
I hope this will help.